Harish-Chandra Research Institute
Chhatnag Road, Jhusi
Allahabad-211019, U. P.
Phone (Mobile):9415309323
Date of birth: October 1,  1944
Allahabad, India



Positions Held


Teaching Experience

Topology, Functional Analysis, Algebra, Commutative Algebra, Homological Algebra, Algebraic Topology, Homology-Cohomology Theories, Homotopy Theory, Measure and Integration, Real Analysis, Complex Analysis, Discrete Mathematics, Graph Theory, Mathematical Foundation of Computer Science, Data and File Structures, Cohomological Dimension Theory, Differential Geometry.

Area of Specialization

Algebraic and Differential Topology,  Topological and Differentiable Group Actions,  Homology-Cohomology Theories,  Cohomological Dimension Theory, Burnside Rings,  Hopfian and Cohopfian Groups,  Spline Modules.

 Administrative Experience

Professional Memberships

Ph.D. Supervision

The following students obtained their Ph.D./D.Sc. Degrees under my supervision
H.S.Tripathi 1982 University of Allahabad
T.B.Singh 1983 University of Allahabad
R.A.Shukla 1983 University of Allahabad
Mohan Singh 1984 University of Jammu
S.Muttepawar 1984 University of Jammu
R.Krishan 1985 University of Jammu
D.S.Jamwal 1986 University of Jammu
P.Palanichamy 1987 University of Jammu
A.N.Roy 1988 University of Allahabad
J.S.Andotra 1989 University of Jammu
C.S.Vaid 1989 University of Jammu
L.Mazumdar 1997 R.D.University,  Jabalpur
J.K.Maitra 1997 R.D.University,  Jabalpur
Dr.M.Shrivastava (D.Sc.)  1997 R.D.University,  Jabalpur sdeo-cv

Three more students are working at Jabalpur.




Research Projects Completed/in Progress


 Visiting Appointments


Seminars,  Conferences Attended/Participated

1. DAE Seminar on ``Global Differential Geometry'' at the University of Mysore, Summer 1982.
2  Instructional Conference on ``Homological Methods in Commutative Algebra, TIFR, Bombay, Summer 1971.
3. Seminar in Algebra,  Kurukschetra University, Kurukschetra,  1975.
4. Seminar in Analysis, Panjab University, Chandigarh, 1976.
5. American Math Society annual Meetings at Dallas (Jan1973), Atlanta ( January, 1978).
6. Mathematical Association of America,  regional meetings at Norman,  Oklahoma 72,  Conway,  Arkansas, 73.
7. Indian Mathematical Society annual meetings at Allahabad, 82, Bhagalpur, 83, Jaipur, 86, Delhi 89, Muzaffarpur,  93, Pune,  94, Aligarh,  95; Rewa 99, Aurangabad 2000.
8. Indian Science Congress Annual conferences at IIT,  Bombay,  1968, Varanasi,  1981,  Ranchi,  1985,  Delhi,  1986,  Bangalore,  1987.
 9. International Symposium on Spline Theory and its Applications at Jabalpur University,  Jabalpur,  Dec 1982.
10. Symposium on ``Recent Advances in Topological and Bitopological spaces'', University of Delhi, 1982.
11. DMV Seminar on ``Surgery Theory and Geometry of Representations'' Dusseldorff, West Germany, July 1987.
12. The UGC Instructional Conference in Algebraic and Differential Topology, Allahabad, Feb 8-28, 1988.
13. The NBHM Instructional Conference on Numerical and Finite Element Methods, IGNOU, New Delhi, Oct 22-Nov 2, 1991.
14. International Conference on Advances in Computational Mathematics, IGNOU, New Delhi, Jan 5-9, 1993.
15. Canadian Mathematical Society summer meetings at Banff, 1994, Calgary 1996.
16. National Conference on Geometry and Topology, R.D.University, Jabalpur, Dec 18-22, 1995.
17. Conference on Topology and Geometry, Indian Institute of Science, Bangalore, Dec 18-23, 1996.
18.  Conference on Novikov Conjecture, ISI,  Calcutta, Dec  98.
19. American Mathematical Society Meeting at Toronto, Canada,  Sep 2000.
20. Conference on Low-Dimensional Topology, University of All'd  and HRI (joint),  All'd  Dec 2000.

Invited Talks Delivered

1. Instructional Conference at the TIFR, Bombay, Summer1971,  one-hour lecture on Regular Local Rings--Nagata's Theorem
2. MRI, Allahabad, Aug 1976,  One hour lecture on Smith Fixed Point Theorems.
3. Department of Mathematics,  IIT, Kanpur, Feb 1975, One hour lecture, On Large cohomological dimensions.
4. University of Arkansas at Pine-Bluff,  Russelville and Conway (77-78), one hour each,on  (i) Cantor Sets (ii) Curves in Planes (iii) Cauchy's Theorem and Homology resp.
5. Colloquium Lectures at Maths Departments of the universities of Allahabad, Jammu,  Arkansas, on Topics of contemporary interests.
6. International Symp. on Spline Theory and Appl., Jabalpur Dec 27-31, 1981, One hour talk, on Compact subsets of real line admitting free Z-actions.
7. Recent Advances on Topological and Bitopological spaces,  Univ of Delhi,  Jan  2-4, 1981,  one hour lecture on Group actions on finitistic spaces.
8. Forty Eigth Annual Conference of the Indian Mathematical Society, Bhagalpur,  Dec    27-30, 1982, one hour lecture on Tautness of cohomology theories.
9. Seventy First Annual Conference of the Indian Science Congress,  Jan 3-8, 1984,  on  Orbit spaces and the Connor Conjecture
10. A series of six seminar lectures at the Indian Statistical Institute , New Delhi,  Summer 1983 on Sheaves,  their cohomology and the cohomological dimensions.
11. Department of Mathematics,  University of Meerut, March 1986,  one-hour lecture on  Development of Category Theory .
12. Society of Mathematical Sciences,  University of Delhi, April 1985,  one hour talk on  Group actions on manifolds
13. Fifty Second Annual Conference of the Indian Mathematical Society Jaipur,  Dec 27-30,  1986, on hour talk on  Converse of Smith fixed point theorems -the smooth case.
14. Seventy Fourth Annual Conference of the Indian Science Congress,  Bangalore,  1987,  half-hour talk on  Completely finitistic paces.
15. A series of four seminar lectures at the Universitat Tubingen,  West Germany,  June 1987,  on  Topology of finitistic spaces.
16. A seminar lecture at the Mathematisches Institute,  Konstanz, West Germany,  June 1987,  one hour,  on  Orbit spaces of finitistic spaces.
17. A Series of nine Seminar-Lectures at the Carleton University,  Ottawa, Sep-Nov 1987 on  Cohomology structure of fixed point  sets and orbit spaces.
18. Colloquium Lecture at the Memorial University,  St John's, New Foundland,  Oct 1987 on  Group Actions and the Hilbert-Smith Conjecure.
19. Colloquium Lecture at the University of St Louis,  St Louis,  Missouri, Oct 1987,  on  Cohomology Theory of Group Actions.
20. Colloquium Lecture at the University of Arkansas,  Fayetteville,  Nov 1987,  on Retraction properties of the orbit spaces.
21. Four one-and-half hour lectures at the NBHM Instructional Conference on Algebraic and Differential Topology at the University of Allahabad,  Feb 8-28, 1988, on  Foundational lectures on Transformation Groups.
23. Two Seminar Lectures at the University of Calgary, Calgary,  Sept 1988,  one hour each,  on  Tautness in cohomology theories .
24 Colloquium Lecture at the Carleton University,  Ottawa,  Dec 1,  1988,  on  Algebraic dimension and the Alexandroff's Problem.
 25. Colloquium Lecture at the University of Calgary,  Dec 15,  1988,  on  Cohomological dimensions and the Alexandroff's Problem.
 26. Annual conference of the Indian Mathematical Society, University of Delhi, Dec 27-30, 1989,  one hour lecture on  Isomorphic Burnside Rings.
27. Conference on Mathematics,  Banaras Hindu University, Varanasi,  Dec 21-22, 1990,  one hour lecture on  Group representations and the Burnside Rings.
28. Two one-hour lectures at the NBHM Instructional Conference at IGNOU,  New Delhi,  Oct 22-Nov 2, 1991, on Dimension of Multivariate Spline Spaces.
29. Three one-hour lectures at the Institute of Technology,  BHU, Varanasi, Jan 1992 on Multivariate splines and their applications.
30. One-hour lecture at the ICODMIC Conference on Geometry at the IIT, New Delhi,  Dec 1993,  on  Cell-like mappings and cohomological dimesion.
31. Three one-hour lectures at the Workshop on Novikov Conjecure at the Indian Statistical Institute,  Calcutta,  Dec 1993,  on  Novikov Conjecture and the cyclic
32. Colloquium Lecture at the University of Hawaii at Manoa,  Summer 1993,  on  Projective dimensions of spline modules.
33. Two one-hour seminar lectures at the University of Calgary,  Summer 1994,  on  Seifert Fiber Bundles and their Fundamental Groups.
34. Two one-hour lectures at the University of Allahabad,  Feb 1995,  on Transformation Groups and the Smith Theory.
35. One hour lecture at the National Conference on Geometry and Topology,  R.D.University,  Jabalpur,  Dec 18-22, 1995 on Cohopficity of the Manifold groups.
36. Colloquium Lecture at the M.S.University,  Baroda,  Jan 1986,  on Discrete Groups and Discontinuous Actions.
37. Colloquium Talk at the University of Auckland,  New Zealand,  April 98 on  Spline modules and their freeness
38. Half hour invited talk at the American Mathematical Society meeting at Toronto,  Sept 2000 on  Free actions on products of spheres.
39. Presidential lecture (General), Indian Mathematical Society Annual Conference at Aurangabad,  Dec 19, 2000.
40. Presidential Lecture (Technical) at the Indian Math Soc Annual Conference at Aurangabad,  Dec 19, 2000,  on Methods of algebraic topology in transformation
41. Twelve Lectures at the University of Arkansas,  USA on Smith Theory,      Fall 2001.

Lectures at the UGC Refresher Courses



1. An example of nonexcisiveness in Sheaf cohomology, Proc. Amer. Math. Soc. 46(1975) 501-503,  MR 52 #1559.
2. On Tautness of Alexander-Spanier cohomology, Proc. Amer. Math. Soc. 2 (1975)441-444,  MR 52 #1670.
3. One-dimensional manifold is of cohomological dimension two, Proc. Amer. Math. Soc. 52(1975) 445-446, MR 52 #15433.
4. Cohomological dimension of an n-manifold is n+1, Pacific J. Math 67 (1976)155-160,  MR 57 #4186.
5. A note on singular cohomology with coefficients in sheaves Math Japonica 21(1976) 229-230, MR 55#6412.
6. On cohomology of simple sheaves, Acta Math.Hung.31(1978) 217-230,  MR 57#13919.
7. On an extension of Localization Theorem and generalized Connor Conjecture Trans. Amer. Math. Soc. 25(1982) 395-402, MR 83a:57501.
8. On the converse of some theorems about orbit spaces, Jour. Lond. Math Soc  25(1982) 162-170,  MR 83k:54039.
9. Compact Lie group actions on finitistic spaces, Topology 21(1982) 391-399,  MR 83k:54042.
10. Sheaf-theoretic cohomological dimensions and finitistic spaces Proc. Amer. Math. Soc. 86(1982) 545-550, MR 84b:55010.
11. On orbit spaces of compact group actions (with P.Palanichamy) Acta Math. Hung. 40(1982) 209-215,  MR 85e:54045.
12. On certain constructions in finitistic spaces (with Mohan Singh) Intern. Jour Math and Math Sci. 3(1983)477-482,  MR 85c:54058.
13. Tautness in sheaf cohomology,  Math. Ann. 263(1983) 221-225, MR 84g:55008.
14. Inverse limit theorem and extension theorem in cohomological dimensions (with S.Muttepawar) Bull Aust Math. Soc. 28(1983) 67-75 MR 85j:55002.
15. Local and global cohomological properties which pass on to the orbit spaces,  Indian Jour. Pure Appl Math. 14(1983) 1319-1326. MR 85h:57049.
16. Cohomological dimension and the sum theorems (with R.A.Shukla) Acta Math Hung 43(1984)17-24,  MR 85h:54040.
17. Countable sum theorems for locally closed sets (with D.S. Jamwal) Bull Aust Math Soc 29(1984) 47-55,  MR 85k:54040.
18. Large cohomological dimension and tauness (with Ram Krishan and D.S.Jamwal) Jour.Aust Math Soc. 17(1985) 49-51,  MR 85k:54041.
19. Completely finitistic spaces are finite dimensional (with A.R.Pears) Bull. London Math. Soc. 17(1985) 49-51,  MR 85k:54041.
20. On Sheaf theoretic cohomological dimension of X and beta(X) (with Subas Muttepawar) Indian J. Math 27(1985)248-253, MR 87i:55002.
21. Finitistic and locally finitistic spaces (with Mohan Singh and D.S.Jamwal) Indian J. Math  27(1985) 183-194,  MR 87i:54101.
22. On tautness and the Subset theorem for large cohomological dimension (with Ram Krishan) Bull Calcutta Math Soc. 77(1985) 248-253,  MR 87i  :55002.
23. On compactly dominated spaces (with Ram Krishan)Acta Math Hung 47(1986) 301-319,  MR 87i:54054.
24. A note on twisted products,  Indian J. Math  29(1987)59-63,  MR 88g:22001.
25. The converse of Smith fixed point theorems -- the smooth case, Math Student 55(1987) 177-181.MR 91c:01042.
26. Cohomologies with exotic supports and the generalised excision (with Ram Krishan and D.S.Jamwal) Jour. Aust Math Soc. 45(1988) 326-340,  MR 89h:55010.
27. Tautness and locally finitely-valued Alexander-Spanier cochains (with A.N.Roy) Proc Amer Math Soc 102(1988)425-430,  MR 89c:55007
28. On cohomological dimension of a space and its Stone-Cech Compactification (with S.Muttepawar) Colloq. Math LV(1988)35-39, MR 89i:54046.
29. On completely finitistic spaces (with J.S.Andotra) Bull Cal Math Soc. 80(1988)173-177,  MR 89k:54022.
30. On equivariant co-homology theories (with A.N Roy) Bull Calcutta Math Soc 79(1987)170-179,  MR 89e:55014.
31. On cotaut subspaces (with Chander Shekhar) Bull Calcutta Math. Soc 81(1989)203-210,  MR 90i:55003.
32. Some examples of non-taut subspaces (with K.Varadarajan) Pacific J. Math 147(1991)47-56,  MR91k:55006.
33. Isomorphic Burnside rings (with K.Varadarajan) J. Algebra 139(1991) 468-483,  MR 92d:20010.
34. On G-finitistic spaces and related notions (with J.S.Andotra) Inter. Jour. Math and Math. Sciences 15(1992)371-378,  MR 93i:54031.
35. Countably finitistic spaces, Bull Calcutta Math. Soc. 84(1992)549-556, MR 93m:54039.
36. Cohomology projective spaces of finite cohomological dimension need not be finitistic, Letters,  National Acad  of Sciences,  India 15(1992)45-48,  MR94c:55001.
37. Invariance of dimension of multivariate spline spaces, Jour. Indian Math Soc. 60(1994)71-81,  MR 95g:41047.
38. On hopfian and cohopfian zero-dimensional spaces (with K. Varadarajan) Jour. Ramanujan Math Soc. 9(1994)177-202,  MR 95j:54020.
39. On projective dimension of spline modules, J. Approx Theory 84(1996) 12-30. 40. Homogenization of ideals in multivariate spline rings (with L. Mazumdar) Jour Indian Math Soc. 62(1996)149-162.
41. Isomorphic Burnside rings II (with K.Varadarajan),  J. Orissa Math Soc Prof Mohanty Felicitation Volume 12-15(1993-96)291-299.
42. Discrete groups and discontinuous actions (with K.Varadarajan) Rocky Mount J. Math 27(1997)559-593.
43. On projective dimension of multivariate splines on Manifolds, Math Student, 65(1996), 166-175.
44. On hopfian and cohopfian groups (with K.Varadarajan), Bull Aust Math Soc. 56(1997)17-24.
45. Automorphism groups of truncated polynomial algebras,  (with J.K.Maitra) National Acad Sciences Letters 20(1997)95-80  ,
46. An algorithm for constructing a basis for C^{r}-spline modules over polynomial rings,  Mathematics of Computation (with L.Mazumdar), 67 (1998) 1107-1120.
47. Free actions of finite groups on products of symmetric powers of even spheres (with  J.K.Maitra),  Proc. Amer. Math. Soc. 128(1999)299-306.
48. Some finiteness properties of groups and their automorphism groups, (with K.Varadarajan and P. Sankaran), Algebra Colloquium 7(2000)411-424.
49. On the torsion of the group of homeomorphisms of the powers of Long Line (with David Gauld) J. Aust Math Soc 70(2000)311-322.

  Expository papers and books

1. Mathematics and Intuition, Bull., Allahabad,  1(1968) 1-10.
2. Cohomology of sheaves and cohomological dimensions, University of Allahabad Studies,  9(1977)131-139.
3. Topology of finitistic spaces, Bull of Allahabad Math Soc. 2(1987)37-61,  MR 91k:54011.
4. Lectures on Transformation Groups, Proc. Allahabad Conference on Algebraic and Differential Topology,  1988.
5. Finiteness properties of groups and their automorphism groups, COSSIST LecturesJadavpur University,  Calcutta,  1997.
6. Algebraic Topology -- a Primer,  Hindustan Book Agency, New Delhi, 2003.TRIM Series #27


1. G.E. Bredon,  Sheaf Theory, Springer Verlag,  Graduate Texts in Mathematics  (1997) refers on pages 171 and 463 to one of my results on Large Cohomological Dimensions proved in : Satya Deo,  Pacific J. Math 67 (1976)155-160.
2. C.Allday and V.Puppe,  Cohomological Methods in Transformation Groups, Cambridge University Press 1993,  refers,  on page 143,  to our work on orbit spaces of finitistic spaces : Satya Deo and H.S. Tripathi,  Topology21(1982) 393-399.
3. E.H. Spanier,  Tautness for Alexander-Spanier Cohomology,  Pacific J. Math 75 (1978) has given an alternative proof of one of my results proved in : Satya Deo, Proc Amer Math Soc 52(1975)441-444.
4. V.I. Kuzminov and A.I. Svedov have generalized ( Dokl SSSR 17(1986) one of our results on Large Cohomological  Dimension proved in :Satya Deo,  Proc. Amer Math Soc 52(1975) 445-449.
5. Rainer Loewen has used, in his paper Journ. fur Riene und Angwandte(1985), our results on cohomological dimensions proved in : Satya Deo and T.B. Singh, Jour London Math Soc 25(1982) 162-170.
6. Y.Hattori,  Questions and Answers in General Topology 3(1985), has used three of our papers on finitistic spaces which appeared in Bull London Math Soc
17(1985)  49-51,  Topology 21(1982) 393-399,  and Int J Math and Math   Sciences.