Abstract
In this chapter, we explain the sheaf-theoretic approach to intersection homology theory. We introduce here the Deligne intersection cohomology complex, whose hypercohomology computes the intersection homology groups. This complex of sheaves can be described axiomatically in a way that is independent of the stratification or any additional geometric structure (such as a piecewise linear structure), leading to a proof of the topological invariance of intersection homology groups.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Banagl, M.: Topological Invariants of Stratified Spaces. Springer Monographs in Mathematics. Springer, Berlin (2007)
BeıÌlinson, A.A., Bernstein, J.N., Deligne, P.: Faisceaux pervers. In: Analysis and Topology on Singular Spaces, I (Luminy, 1981). Astérisque, vol. 100, pp. 5â171. Soc. Math. France, Paris (1982)
Borel, A.: Intersection cohomology. Modern BirkhÀuser Classics. BirkhÀuser Boston, Inc., Boston, MA (2008)
Borho, W., MacPherson, R.: Partial resolutions of nilpotent varieties. In: Analysis and Topology on Singular Spaces, II, III (Luminy, 1981). Astérisque, vol. 101, pp. 23â74. Soc. Math. France, Paris (1983)
Cappell, S.E., Shaneson, J.L.: Singular spaces, characteristic classes, and intersection homology. Ann. Math. (2) 134(2), 325â374 (1991)
Dimca, A.: Singularities and Topology of Hypersurfaces. Universitext. Springer, New York (1992)
Dimca, A.: Sheaves in Topology. Universitext. Springer, Berlin (2004)
Durfee, A.H.: Intersection homology Betti numbers. Proc. Am. Math. Soc. 123(4), 989â993 (1995)
Friedman, G.: An introduction to intersection homology with general perversity functions. In: Topology of Stratified Spaces. Mathematical Sciences Research Institute Publications, vol. 58, pp. 177â222. Cambridge University Press, Cambridge (2011)
Goresky, M., MacPherson, R.: Intersection homology. II. Invent. Math. 72(1), 77â129 (1983)
Goresky, M., Siegel, P.: Linking pairings on singular spaces. Comment. Math. Helv. 58(1), 96â110 (1983)
Hurewicz, W., Wallman, H.: Dimension Theory. Princeton Mathematical Series, v. 4. Princeton University Press, Princeton, N. J. (1941)
Maxim, L.: A decomposition theorem for the peripheral complex associated with hypersurfaces. Int. Math. Res. Not. 43, 2627â2656 (2005)
Maxim, L.: Intersection homology and Alexander modules of hypersurface complements. Comment. Math. Helv. 81(1), 123â155 (2006)
Rietsch, K.: An introduction to perverse sheaves. In: Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry. Fields Inst. Commun., vol. 40, pp. 391â429. American Mathematical Society, Providence, RI (2004)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Maxim, L.G. (2019). Intersection Homology After Deligne. In: Intersection Homology & Perverse Sheaves. Graduate Texts in Mathematics, vol 281. Springer, Cham. https://doi.org/10.1007/978-3-030-27644-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-27644-7_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-27643-0
Online ISBN: 978-3-030-27644-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)