Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T21:24:38.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Intersection K-theory for isolated conical singularities

Published online by Cambridge University Press:  18 February 2011

André Legrand  and
David Poutriquet
André Legrand
Affiliation:
Université de Toulouse, Institut de Mathématiques de Toulouse (UMR 5219), 118 Route de Narbonne F-31062 Toulouse Cedex, France, andre.legrand@math.univ-toulouse.fr
David Poutriquet
Affiliation:
Université de Toulouse, Institut de Mathématiques de Toulouse (UMR 5219), 118 Route de Narbonne F-31062 Toulouse Cedex, France, david.poutriquet@math.univ-toulouse.fr
Get access

Abstract

Starting from the Karoubi multiplicative K-theory, we construct a Chern-Weil theory adapted to isolated conical singularities. The Chern character takes its values in the intersection cohomology of Goresky-MacPherson. We also propose an integer intersection K-theory for such singularities.

Keywords

Chern characterK-theoryintersection homologyconical singularities
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 1 , February 2012 , pp. 177 - 200
Copyright
Copyright © ISOPP 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Atiyah, M. F., Hirzebruch, F.. Vector bundles and homogeneous spaces, Proc. Symp. in Pure Math., Amer. Math. Soc. 3 (1961), 7–38.Google Scholar
2.Brasselet, J.P. Homologie d'intersection, définition singulière et simpliciale, Séminaire Ecole Polytechnique (1984–1985).Google Scholar
3.Brasselet, J.P.. de Rham theorems for singular manifolds, Contemp. Math. 161 (1994), 95–112.CrossRefGoogle Scholar
4.Brasselet, J.P., Goresky, M. and MacPherson, R.. Simplicial Differential Forms with Poles, Amer. Journal of Math. 113 (1991), 1019–1052.CrossRefGoogle Scholar
5.Brasselet, J.P., Legrand, A.. Un complexe de formes différentielles à croissance bornée sur une variété statifiée, An. Sc. N. Pisa, Serie IV, Vol XXI, Fasc 2 (1994), 213–234.Google Scholar
6.Brasselet, J.P., Legrand, A, Teleman, N.. Hochshild homology of singular algebras, K-Theory 29 (2003), 1–25.CrossRefGoogle Scholar
7.Cheeger, J.. On the Hodge theory of riemannian spaces, Proc. Symp. in Pure Math., Amer. Math. Soc. 36 (1980), 91–146.Google Scholar
8.Connes, A.. Noncommutative geometry, Academic Press, Inc., San Diego, CA, 1994.Google Scholar
9.Debord, C., Lescure, J.M.. K-duality for pseudomanifolds with isolated singularities, J. Funct. Anal. 219 (2005), 109–133.CrossRefGoogle Scholar
10.Goresky, M., MacPherson, R.. Intersection homology theory, Topology 19 (1980), 135–162.CrossRefGoogle Scholar
11.Karoubi, M.. Homologie cyclique et K-Théorie, Astérisque 149 (1987).Google Scholar
12.Karoubi, M.. Théorie générale des classes caractéristiques secondaires, K-Theory 4 (1990), 55–87.CrossRefGoogle Scholar
13.Karoubi, M.. Classes caractéristiques de fibrés feuilletés, holomorphes ou algébriques, K-Theory 8 (1994), 153–211.CrossRefGoogle Scholar
14.Legrand, A., Poutriquet, D.. K-théorie pour les singularités coniques isolées, C. R. Math. Acad. Sci. Paris 341, no. 12 (2005), 751–754.CrossRefGoogle Scholar
15.Poutriquet, D.. K-théorie des singularités coniques isolées. Thèse de l'Université Paul Sabatier, Toulouse (2006).Google Scholar
16.Youssin, B.. Lp-cohomology of cones and horns, J. Differential Geom. 39, no. 3 (1994), 559–603.CrossRefGoogle Scholar