Research Publications:

  1. An example of nonexcisiveness in Sheaf cohomology, Proc. Amer. Math. Soc. 46 (1975) 501-503.
  2. On Tautness of Alexander-Spanier cohomology, Proc. Amer. Math. Soc. 52 (1975) 441-444.
  3. One-dimensional manifold is of cohomological dimension two, Proc. Amer. Math. Soc. 52 (1975) 445-446.
  4. Cohomological dimension of an n-manifold is n+1, Pacific J. Math 67 (1976) 155-160.
  5. A note on singular cohomology with coefficients in sheaves Math Japonica 21 (1976) 229-230.
  6. On cohomology of simple sheaves, Acta Math. Hung. 31 (1978) 217-230.
  7. On an extension of Localization Theorem and generalized Connor Conjecture ( with T.B.Singh and R.A. Shukla) Trans. Amer. Math. Soc. 25 (1982) 395-402.
  8. On the converse of some theorems about orbit spaces, (with T.B.Singh) Jour. Lond. Math. Soc.  25 (1982) 162-170.
  9. Compact Lie group actions on finitistic spaces (with H.S. Tripathi) Topology 21 (1982) 391-399.
  10. Sheaf-theoretic cohomological dimensions and finitistic spaces Proc. Amer. Math. Soc. 86 (1982) 545-550.
  11. On orbit spaces of compact group actions (with P.Palanichamy) Acta Math. Hung. 40 (1982) 209-215.
  12. On certain constructions in finitistic spaces (with Mohan Singh) Intern. Jour Math and Math Sci. 3 (1983) 477-482.
  13. Tautness in sheaf cohomology,  Math. Ann. 263 (1983) 221-225.
  14. Inverse limit theorem and extension theorem in cohomological dimensions (with S.Muttepawar) Bull Aust Math. Soc. 28 (1983) 67-75.
  15. Local and global cohomological properties which pass on to the orbit spaces,  Indian Jour. Pure Appl Math. 14 (1983) 1319-1326.
  16. Cohomological dimension and the sum theorems (with R.A.Shukla) Acta Math Hung.  43 (1984) 17-24.
  17. Countable sum theorems for locally closed sets (with D.S. Jamwal) Bull Aust Math. Soc.  29 (1984) 47-55.
  18. Large cohomological dimension and tauness (with Ram Krishan and D.S.Jamwal) Jour. Aust Math Soc.  17 (1985) 49-51.
  19. Completely finitistic spaces are finite dimensional (with A.R.Pears) Bull. London Math. Soc. 17 (1985) 49-51.
  20. On Sheaf theoretic cohomological dimension of X and beta(X) (with Subas Muttepawar) Indian J. Math 27 (1985) 248-253.
  21. Finitistic and locally finitistic spaces (with Mohan Singh and D.S.Jamwal) Indian J. Math.  27 (1985) 183-194.
  22. On tautness and the Subset theorem for large cohomological dimension (with Ram Krishan) Bull Calcutta Math Soc. 77 (1985) 248-253.
  23. On compactly dominated spaces (with Ram Krishan) Acta Math Hung  47 (1986) 301-319.
  24. A note on twisted products, Indian J. Math   29 (1987) 59-63.
  25. The converse of Smith fixed point theorems - the smooth case, Math Student  55 (1987) 177-181.
  26. Cohomologies with exotic supports and the generalised excision (with Ram Krishan and D.S.Jamwal) Jour. Aust Math Soc. 45 (1988) 326-340.
  27. Tautness and locally finitely-valued Alexander-Spanier cochains (with A.N.Roy) Proc Amer Math Soc  102 (1988) 425-430.
  28. On cohomological dimension of a space and its Stone-Cech Compactification (with S.Muttepawar) Colloq. Math LV (1988) 35-39.
  29. On completely finitistic spaces (with J.S.Andotra) Bull Calcutta Math Soc. 80 (1988) 173-177
  30. On equivariant co-homology theories (with A.N Roy) Bull Calcutta Math Soc  79 (1987) 170-179.
  31. On cotaut subspaces (with Chander Shekhar) Bull Calcutta Math. Soc 81 (1989) 203-210
  32. Some examples of non-taut subspaces (with K.Varadarajan) Pacific J. Math  147 (1991) 47-56.
  33. Isomorphic Burnside rings (with K.Varadarajan) J. Algebra 139 (1991) 468-483.
  34. On G-finitistic spaces and related notions (with J.S.Andotra) Inter. Jour. Math and Math. Sciences 15 (1992) 371-378.
  35. Countably finitistic spaces, Bull Calcutta Math. Soc.  84 (1992) 549-556.
  36. Cohomology projective spaces of finite cohomological dimension need not be finitistic, Letters, National Academy  of Sciences,  India  15 (1992) 45-48.
  37. Invariance of dimension of multivariate spline spaces, Jour. Indian Math Soc. 60 (1994) 71-81.
  38. On hopfian and cohopfian zero-dimensional spaces (with K. Varadarajan) Jour. Ramanujan Math Soc.  9 (1994) 177-202.
  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 hopfian and cohopfian groups (with K.Varadarajan), Bull Aust Math Soc.  56 (1997) 17-24.
  44. Automorphism groups of truncated polynomial algebras,  (with J.K.Maitra) National Acad Sciences Letters 20 (1997) 95-80 .
  45. An algorithm for constructing a basis for C^{r}-spline modules over polynomial rings, (with L.Mazumdar) Mathematics of Computation , 67 (1998) 1107-1120.
  46. 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.
  47. Some finiteness properties of groups and their automorphism groups, (with K.Varadarajan and P. Sankaran), Algebra Colloquium 7 (2000) 411-424.
  48. On the torsion of the group of homeomorphisms of the powers of Long Line (with D. Gauld) J. Aust Math Soc.  70 (2000) 311-322.
  49. Spline modules from a divided domain to a subdivided domain, (with J. K. Maitra) Indian J. Pure Appl. Math. 35 (2004) 1033-1041.
  50. Strongly contractible polyhedra which are not simply contractible for any n > 1 (with V. V. Awasthi), J. Indian Math Soc. 72 (2005) 75-82. 
  51. Freeness of homomogenized spline module from a divided domain to a subdivided domain (with J. K. Maitra) Frontiers in Interpolation and Approximation, Ed. N. K. Govil et al., Taylor and Francis, (2006) 59-74.
  52. Hilbert Series of free spline modules (with J. K. Maitra) J. Indian Math Soc. 73 (2006)53-64.
  53. Eventually constant spaces and nonmetrizable homology spheres (with David Gauld) J. Indian Math Soc, Special Centenary Volume (2008)165-175.
  54. An inverse system of nonempty objects with empty limit (with V.V.Awasthi) Indian J Math 51 (2009) 689-697.
  55. Mapping class groups of powers of the Long Ray and other nonmetrizable manifolds(with M.Baillif and D.Gauld), Topology and Applications 157(2010)1314-1324.
  56. Index of a finitistic space and a generalization of the topological central point theorem, Journal of Ramanujan Mathematical Society, 28(2013)223-232.
  57. Combinatorial 8-manifolds like quarternionic projective planes and their nonembeddings, New Zealand Journal of Mathematics, 44(2014)53-58.
  58. Topological Combinatorics-The Kneser Conjecture, Math Student 83(2014)01-16.
  59. Topological Combinatorics- Birch-Tverberg Theorem and its generalizations, Clifford Algebra, Clifford Analysis and its Applications, 4(2015), 273-283.
  60. The Topological Colored Tverberg Theorem and the Reduction Lemma, arXiv, 1502.04805, Feb 2015.
  61.  Colored Topolgical Tverberg Theorem of Blagojevi´c, Matschke and Ziegler, Math. Student, 84(2015),149-158.
  62.  Boundedly Metacompact or Finitistic spaces and the Star order of Covers, (with David Gauld), J. Indian Math Soc, 83(2016),01-20.
  63.  

        

 

         Preprints

  1. Homology and Dimension- further pathological examples (with V.V.Awsthi)
  2. Branched coverings, label led coverings, and transitive permutation groups (with R.S.Kulkarni), in preparation.
  3. Strong Indepencence and the dimension of Tverberg set (Snigdha Choudhury)

 

Expository papers:

  1. Cohomology of sheaves and cohomological dimensions, University of Allahabad Studies 9 (1977) 131-139.
  2. The converse of Smith fixed point theprems - the smooth case, Math student 55 (1987) 177-181.
  3. Topology of finitistic spaces, Bull. of Allahabad Math. Soc. 2 (1987) 37-61.
  4. Lectures on Transformation Groups, Proc. Allahabad Conference on Algebraic and Differential Topology, 1988.
  5. On projective dimension of multivariate splines on manifolds, Math. Student, 65 (1996) 166-175.
  6. Finiteness properites of groups and their automorphism groups, COSSIST, Lectures, Jadavpur University, Calcutta, 1997.
  7. Cohomology Theories best suited for algebraic dimension theories, Math Student, Special Centenary volume (2007) 121-134.
  8. Why do we call them projective spaces? Ramanujan Mathematical Society News Letter,  2008

 

Books written:

Algebraic Topology- a primer, Hindustan Book Agency, TRIM Series - No.27(2003), 2nd printing, 2006, New Delhi.

Algebraic Topology- A Primer, Second Edition, Hindustan Book Agency, Trim Series No 27 (2018), New Delhi.

 

Citations:

  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.PuppeCohomological 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,  Topology 21(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.

 

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