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Goresky, Mark; MacPherson, Robert

Intersection homology. II. (English) Zbl 0529.55007

Invent. Math. 72, 77-129 (1983).
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Cited in 26 Reviews
Cited in 280 Documents

MSC:

55N35 Other homology theories in algebraic topology
55N30 Sheaf cohomology in algebraic topology
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14F45 Topological properties in algebraic geometry
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
58A35 Stratified sets
57N80 Stratifications in topological manifolds
32Sxx Complex singularities

Keywords:

intersection homology groups for singular spaces; perversity; stratification; chain complexes of sheaves; hypercohomology; hyperplane sections; Deligne construction; duality

Citations:

Zbl 0448.55004
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Full Text: DOI EuDML

References:

[1] Artin, M.: Théorème de finitude pour un morphisme propre: dimension cohomologique des schemas algébriques affines, EGA4, expose XIV. Lecture Notes in Mathematics vol. 305. Berlin-Heidelberg-New York: Springer 1973
[2] Andreotti, A., Frankel, T.: The Lefschetz theorem on hyperplane sections. Annals of Mathematics69, 713-717 (1959) · Zbl 0115.38405 · doi:10.2307/1970034
[3] Barthel, G., Georinger, G., Duskin, J., Fittler, R., Acuña, H., Gergondey, R., Verdier, J.L., Zisman, M.: Dualité de Poincaré. Séminaire Heidelberg-Strasbourg 1966/67. Publ. I.R.M.A., 5, rue R. Descartes, 67-Strasbourg
[4] Bredon, G.: Sheaf theory. New York: McGraw-Hill 1967 · Zbl 0158.20505
[5] Borel, A.: Seminar on transformation groups. Annals of Mathematics Studies, no. 46, Princeton University Press, Princeton, NJ 1960 · Zbl 0091.37202
[6] Borel, A., Moore, J.C.: Homology theory for locally compact spaces. Michigan Math J.7, 137-159 (1960) · Zbl 0116.40301 · doi:10.1307/mmj/1028998385
[7] Borho, W., MacPherson, R.: Représentations des groupes de Weyl et homologie d’intersection pour les variétés nilpotentes. C.R. Acad. Sci. Paris, t. 292 Ser. I, 707-710 (1981) · Zbl 0467.20036
[8] Cartan, H., Chevalley, C.: Séminaire de Géometrie Algébrique. Ecole Normale Superieure, Paris 1956
[9] Cartan, H., Eilenberg, S.: Homological algebra. Princeton University Press, Princeton, NJ 1956 · Zbl 0075.24305
[10] Cheeger, J.: On the Hodge theory of Riemannian pseudomanifolds. In: Geometry of the laplace operator. Proceedings of Symposia in pure Mathematics36, 91-146 (1980). Amer. Math. Soc. Providence, RI · Zbl 0461.58002
[11] Cheeger, J., Goresky, M., MacPherson, R.:L 2 Cohomology and intersection homology of singular algebraic varieties. Seminar on differential geometry, Yau, S.T. (ed.) Princeton University Press, Princeton, NJ 1982 · Zbl 0503.14008
[12] Deligne, P.: Théorème de Lefschetz et critères de dégénérescence de suites spectrales. Publ. Math. I.H.E.S.35, 107-126 (1968) · Zbl 0159.22501
[13] Deligne, P.: Théorie de Hodge II, Publ. Math. I.H.E.S.40, 21 (1971) · Zbl 0219.14007
[14] Deligne, P.: Letter to D. Kazhdan and G. Lusztig dated 20 April 1979
[15] Fulton, W., MacPherson, R.: Categorical framework for the study of singular spaces. Memoirs of the Amer. Math. Soc. vol. 243 A.M.S., Providence, RI 1981 · Zbl 0467.55005
[16] Gelfand, S., MacPherson, R.: Verma modules and Schubert cells: a dictionary, Seminaire d’Algebra. Lecture Notes in Mathematics vol. 924. Berlin-Heidelberg-New York: Springer 1982 · Zbl 0512.22009
[17] Godement, R.: Topologie algébrique et théorie des faisceaux. Paris: Hermann, 1958 · Zbl 0080.16201
[18] Goresky, M.: Whitney stratified chains and cochains. Trans. Amer. Math. Soc.267, 175-196 (1981) · Zbl 0476.57019 · doi:10.1090/S0002-9947-1981-0621981-X
[19] Goresky, M., MacPherson, R.: La dualité de Poincaré pour les espaces singuliers. C.R. Acad. Sci. t.284, (Serie A) 1549-1551 (1977) · Zbl 0402.55010
[20] Goresky, M., MacPherson, R.: Intersection homology theory. Topology19, 135-162 (1980) · Zbl 0448.55004 · doi:10.1016/0040-9383(80)90003-8
[21] Goresky, M., MacPherson, R.: Stratified Morse theory. Proceedings of A.M.S. conference in Singularities at Arcata Calif. 1981 · Zbl 0526.57022
[22] Hamm, H.: Lokale topologische Eigenschaften komplexer Räume. Math. Ann.191, 235-252 (1971) · Zbl 0214.22801 · doi:10.1007/BF01578709
[23] Hartshorne, R.: Residues and duality. Lecture Notes in Mathematics vol. 20. Berlin-Heidelberg-New York: Springer 1966 · Zbl 0212.26101
[24] Hurewicz, W., Wallman, H.: Dimension theory. Princeton University Press, Princeton, NJ 1941 · JFM 67.1092.03
[25] Iverson, B.: Cohomology of sheaves, preprint, Aarhus, Denmark (1976)
[26] Kato, M.: Partial Poincaré duality fork-regular spaces and complex algebraic sets. Topology16, 33-50 (1977) · Zbl 0367.14009 · doi:10.1016/0040-9383(77)90029-5
[27] Kaup, L.: Nachr. Adad. Wiss. Göttingen Math-Phys. Kl.II, 213-224, 1966
[28] Kaup, L.: Exakte Sequenzen für globale und lokale Poincaréhomomorphismen. Real and Complex Singularities (P. Holm, ed.) Sitjthoff and Noordhoff Publ., Norway 1978
[29] McCrory, C.: Stratified general position. Algebraic and geometric topology. Lecture Notes in Mathematics, vol. 664, pp. 142-146. Berlin-Heidelberg-New York: Springer 1978
[30] Mather, J.: Stratifications and mappings. Dynamical systems Peixoto, M.M. (ed.). New York: Academic Press 1973 · Zbl 0286.58003
[31] Milnor, J.: Morse theory, Annals of Mathematics Studies no. 51, Princeton University Press (1969), Princeton, New Jersey
[32] Narasimhan, R.: On the homology groups of Stein Spaces. Invent. Math.2, 377-385 (1967) · Zbl 0148.32202 · doi:10.1007/BF01428900
[33] Ogus, A.: Local cohomological dimension of algebraic varieties. Annals of Mathematics98, 327-366 (1973) · Zbl 0308.14003 · doi:10.2307/1970785
[34] Oka, M.: On the cohomology structure of projective varieties, in Manifolds?Tokyo, 1973. Hattori, A. (ed.). University of Tokyo Press, 1975
[35] Siegel, P.: Witt spaces, a geometric cycle theory for KO homology at odd primes. Ph.D. thesis (M.I.T.), 1979. (To appear in Amer. J. of Math.) · Zbl 0547.57019
[36] Siebenmann, L.: Deformations of homeomorphisms on stratified sets. Comm. Math. Helvetici47, 123-163 (1972) · Zbl 0252.57012 · doi:10.1007/BF02566793
[37] Steenrod, N.: The topology of fibre bundles. Princeton Mathematical series no. 14, Princeton University Press, Princeton, NJ 1951 · Zbl 0054.07103
[38] Swan, R.: The theory of sheaves. Chicago Lectures in Mathematics, University of Chicago Press, Chicago, 1964 · Zbl 0119.25801
[39] Tennison, B.: Sheaf Theory. London Mathematical Society Lecture Note Series vol. 20, Cambridge University Press, 1975 · Zbl 0313.18010
[40] Thom, R.: Ensembles et morphismes stratifiés. Bull, Amer. Math. Soc.75, 240-284 (1969) · Zbl 0197.20502 · doi:10.1090/S0002-9904-1969-12138-5
[41] Verdier, J.L.: Le théorème de dualité de Poncaré. C.R. Acad. Sci.256 (1963)
[42] Verdier, J.L.: Dualité dans la cohomologie des espaces localment compactes. Séminar Bourbaki vol.300 (1965)
[43] Verdier, J.L.: Categories derivées, État 0. SGA 4 1/2. Lecture Notes in Mathematics vol. 569. Berlin-Heidelberg-New York: Springer 1977
[44] Verdier, J.L.: Dimension des espaces localement compacts. C.R. Acad. Sci. Paris t.261, 5293-5296 (1965) · Zbl 0171.21501
[45] Verdier, J.L.: Faisceaux constructibles sur un espace localement compact. C.R. Acad. Sci. Paris t.262 (1966) · Zbl 0171.21405
[46] Vilonen, K.: Master’s thesis. Brown University, Providence, R.I. (1980)
[47] Wilder, R.L.: Topology of manifolds. Amer. Math. Soc. Publ. no.32, Providence, RI (1949) · Zbl 0039.39602
[48] Zeeman, C.: Dihomology I and II. Proc. London Math. Soc. (1)12, 609-638, 639-689 (1962) · Zbl 0109.41302 · doi:10.1112/plms/s3-12.1.609
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