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, 25:7 | Cite as

The L-homology fundamental class for IP-spaces and the stratified Novikov conjecture

  • Markus Banagl
  • Gerd LauresEmail author
  • James E. McClure
Article
  • 4 Downloads

Abstract

An IP-space is a pseudomanifold whose defining local properties imply that its middle perversity global intersection homology groups satisfy Poincaré duality integrally. We show that the symmetric signature induces a map of Quinn spectra from IP bordism to the symmetric L-spectrum of \({\mathbb {Z}}\), which is, up to weak equivalence, an \(E_\infty \) ring map. Using this map, we construct a fundamental L-homology class for IP-spaces, and as a consequence we prove the stratified Novikov conjecture for IP-spaces whose fundamental group satisfies the Novikov conjecture.

Keywords

Intersection homology Stratified spaces pseudomanifolds Signature Characteristic classes Bordism L-theory Novikov conjecture 

Mathematics Subject Classification

55N33 57R67 57R20 57N80 19G24 

Notes

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Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany
  2. 2.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA

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