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. 2 (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 spacse, (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 Cal 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 Acad  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 Analysis, Clifford Algebras and their Applications, 4(2015)273-283..
  60. Topological Coloured Theorem and the Reduction Lemma, arXiv 1502.04805, Feb 2015.
  61. Colored Topological Tverberg Theorem of  Blagojeviīc, 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., 84(2016), 01-20.

 

          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.

 

 

Expository papers:

  1. Cohomology of sheaves and cohomological dimensions, University of Allahabad Studies 9 (1977) 131-139.
  2. The converse of Smith fixed point theorems - 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 properties 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:

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

2.      Algebraic Topology- a primer, Second Edition, HBA, TRIM series- 2017, New Delhi.

 

Important 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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