Zeeman’s filtration of homology

McCrory, Clint

doi:10.1090/S0002-9947-1979-0530047-X

Zeeman’s filtration of homology
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Trans. Amer. Math. Soc. 250 (1979), 147-166 Request permission

Abstract:

Geometric interpretations of Zeeman’s filtrations of the homology and cohomology of a triangulable space are given, using an analysis of his spectral sequence for Poincaré duality.

References

Ethan Akin, Manifold phenomena in the theory of polyhedra, Trans. Amer. Math. Soc. 143 (1969), 413–473. MR 253329, DOI 10.1090/S0002-9947-1969-0253329-1
Glen E. Bredon, Sheaf theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0221500
Eduard Čech, Multiplications on a complex, Ann. of Math. (2) 37 (1936), no. 3, 681–697. MR 1503304, DOI 10.2307/1968483
W. W. Flexner, Simplicial intersection chains for an abstract complex, Bull. Amer. Math. Soc. 46 (1940), 523–524. MR 2550, DOI 10.1090/S0002-9904-1940-07253-2

Théorie des faisceaux

Gerald Leonard Gordon, A Poincaré duality type theorem for polyhedra, Ann. Inst. Fourier (Grenoble) 22 (1972), no. 4, 47–58 (English, with French summary). MR 339141, DOI 10.5802/aif.434
Gerald Leonard Gordon, The residue calculus in several complex variables, Trans. Amer. Math. Soc. 213 (1975), 127–176. MR 430297, DOI 10.1090/S0002-9947-1975-0430297-3
Mark Goresky and Robert MacPherson, La dualité de Poincaré pour les espaces singuliers, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 24, A1549–A1551. MR 440533

Homology theory

Mitsuyoshi Kato, Topology of $k$-regular spaces and algebraic sets, Manifolds—Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973) Univ. Tokyo Press, Tokyo, 1975, pp. 153–159. MR 0418105
Mitsuyoshi Kato, Partial Poincaré duality for $k$-regular spaces and complex algebraic sets, Topology 16 (1977), no. 1, 33–50. MR 450607, DOI 10.1016/0040-9383(77)90029-5
Ludger Kaup, Poincaré Dualität für Räume mit Normalisierung, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 26 (1972), 1–31 (German). MR 385152
Ludger Kaup, Zur Homologie projektiv algebraischer Varietäten, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 26 (1972), 479–513 (German). MR 385153
R. D. MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. (2) 100 (1974), 423–432. MR 361141, DOI 10.2307/1971080
John N. Mather, Stratifications and mappings, Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) Academic Press, New York, 1973, pp. 195–232. MR 0368064

Poincaré duality in spaces with singularities

Clint McCrory, Cone complexes and PL transversality, Trans. Amer. Math. Soc. 207 (1975), 269–291. MR 400243, DOI 10.1090/S0002-9947-1975-0400243-7
Clint McCrory, A characterization of homology manifolds, J. London Math. Soc. (2) 16 (1977), no. 1, 149–159. MR 445506, DOI 10.1112/jlms/s2-16.1.149
Clint McCrory, Stratified general position, Algebraic and geometric topology (Proc. Sympos., Univ. California, Santa Barbara, Calif., 1977) Lecture Notes in Math., vol. 664, Springer, Berlin, 1978, pp. 142–146. MR 518413

A topological bound for the Deligne weight

Complément à l’analysis situs

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Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
N. E. Steenrod, Cohomology invariants of mappings, Ann. of Math. (2) 50 (1949), 954–988. MR 31231, DOI 10.2307/1969589
D. Sullivan, Singularities in spaces, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Lecture Notes in Math., Vol. 209, Springer, Berlin, 1971, pp. 196–206. MR 0339241

Problems on singularities

George W. Whitehead, Generalized homology theories, Trans. Amer. Math. Soc. 102 (1962), 227–283. MR 137117, DOI 10.1090/S0002-9947-1962-0137117-6
Hassler Whitney, On products in a complex, Ann. of Math. (2) 39 (1938), no. 2, 397–432. MR 1503416, DOI 10.2307/1968795
S. Wylie, Duality and intersection in general complexes, Proc. London Math. Soc. (2) 46 (1940), 174–198. MR 1904, DOI 10.1112/plms/s2-46.1.174
E. C. Zeeman, Dihomology. I. Relations between homology theories, Proc. London Math. Soc. (3) 12 (1962), 609–638. MR 153009, DOI 10.1112/plms/s3-12.1.609