×

Regular differential forms on stratified spaces. (English) Zbl 0837.55003

Summary: Given a stratified space \(W\), we present for each perversity \(\overline q\) a complex of differential forms which are defined on any stratum, are “regular” with respect to a fixed family of trivializations of \(W\) and whose cohomology is dual to the intersection homology of \(W\) for the complementary perversity \(\overline p\).

MSC:

55N33 Intersection homology and cohomology in algebraic topology
14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] [Bo]A. Borel et al. Intersection Cohomology. Progress in Mathematics vol 50, Birkhäuser, 1984
[2] [BGM]J.P. Brasselet, M. Goresky etR. MacPherson Simplicial Differential Forms with Poles, Amer. Journal of Maths., 113 (1991), 1019–1052 · Zbl 0748.55002
[3] [BHS]J.P. Brasselet, M. Hector etM. Saralegi Théorème de De Rham pour les variétés singulières, Annals of Global Analysis and Geometry Vol. 9, no 3, 1991, 211–243 · Zbl 0733.57010
[4] [Br]J.-L. Brylinski,Equivariant intersection cohomology, Preprint I.H.E.S. (1986), revised as Preprint Pennsylvania State Univ. (1989)
[5] [C]J. Cheeger On the Hodge theory of Riemannian pseudomanifolds, Proc. of Symp. in Pure Math. vol 36 (1980), 91–146. Amer. Math. Soc., Providence R.I.
[6] [CGM]J. Cheeger, M. Goresky andR. MacPherson,L 2-cohomology and intersection cohomology for singular varieties, Sominar on Differential Geometry, S.T. Yau, ed. Ann. of Math. Studies, Princeton University Press, Princeton N.J., 102 (1982), 303–340
[7] [F]M. Ferrarotti,A complex of stratified forms satisfying De Rham’s theorem, to appear in Proc. of Hawaii-Provence Singularities. Springer Lecture Notes · Zbl 0884.58003
[8] [GM1]M. Goresky etR. MacPherson Intersection homology theory. Topology 19 (1980), 135–162 · Zbl 0448.55004
[9] [GM2]M. Goresky etR. MacPherson Intersection homology theory II. Inv. Math. 71 (1983), 77–129 · Zbl 0529.55007
[10] [M]J. Mather,Notes on topological stability, Preprint, Harvard (1970) · Zbl 0207.54303
[11] [N]M. Nagase Sheaf theoreticL 2-cohomology, Adv. Stud. Pure Math.n o 8 (1987), 273–279, North Holland
[12] [O]T. Ohsawa On theL 2-cohomology of complex spaces, Math. Z. 209 (1992), 519–530 · Zbl 0759.58002
[13] [T]R. Thom,Ensembles et morphismes stratifiés, Bull. A.M.S. 75, 240–284 (1969) · Zbl 0197.20502
[14] [V1]A. Verona,Stratified Mappings-Structure and Triangulability, Lecture Notes in Maths. 1102, (1984)
[15] [V2]A. Verona,Sur la cohomologie de DeRham des préstratifications de Whitney, C.R.A.S. Paris 274, 1340–1343 (1972) · Zbl 0244.55004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.