The L-class of non-Witt spaces. (English) Zbl 1101.57013

Banagl, Markus

Ann. Math. (2) 163, No. 3, 743-766 (2006).

This paper defines characteristic classes analogous to the Hirzebruch L-class for non-Witt spaces. To define these classes one needs Lagrangian structures on the strata of odd codimension and the classes are shown to be independent of the Lagrangian structure. This is applied to certain compactifications of locally symmetric spaces.

Reviewer: R. E. Stong (Charlottesville)

MSC:

57R20	Characteristic classes and numbers in differential topology
57N80	Stratifications in topological manifolds
32S60	Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
55N33	Intersection homology and cohomology in algebraic topology

Keywords:

characteristic classes; Hirzebruch L-class; Lagrangian structures; strata; compactifications of locally symmetric spaces