L2-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature

Jeff Cheeger, Xianzhe Dai

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We study from a mostly topological standpoint the L2-signature of certain spaces with nonisolated conical singularities. The contribution from the singularities is identified with a topological invariant of the link fibration of the singularities. This invariant measures the failure of the signature to behave multiplicatively for fibrations for which the boundary of the fiber is nonempty. The result extends easily to cusp singularities and can be used to compute the L2-cohomology of certain noncompact hyperkähler manifolds that admit geometrically fibered end structures.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages1-24
Number of pages24
DOIs
StatePublished - 2009

Publication series

NameProgress in Mathematics
Volume271
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Fingerprint Dive into the research topics of 'L<sup>2</sup>-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature'. Together they form a unique fingerprint.

Cite this