Geometric Analysis and Topology Seminar

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Poincare-Hopf Theorem and Indices of One-Forms for Singular Spaces

Speaker: Joerg Schuermann, University of Munster

Location: Warren Weaver Hall 202

Date: Monday, March 29, 2010, 11 a.m.

Synopsis:

Given a compact singular Whitney stratified subset X of an oriented manifold M, one can associate to a constructible function on X a corresponding conic Lagrangian cycle in the cotangent bundle T*M. This can be done for example with the help of stratified Morse theory in the sense of Goresky-MacPherson. Then one defines for a connected component of the stratified critical locus of a one form on M an index as a micro-local intersection number in T*M. The sum of these indices calculates the Euler characteristic of X weighted by the constructible function. Suitable choices of the constructible function give different notions of indices used in the literature.