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
Volume271
DOIs
StatePublished - Jan 1 2009

Publication series

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

Fingerprint

Conical Singularities
Cohomology
Signature
Fibration
Singularity
Noncompact Manifold
Topological Invariants
Cusp
Invariant Measure
Fiber

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Cheeger, J., & Dai, X. (2009). L2-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature. In Progress in Mathematics (Vol. 271, pp. 1-24). (Progress in Mathematics; Vol. 271). Springer Basel. https://doi.org/10.1007/978-0-8176-4743-8_1

L2-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature. / Cheeger, Jeff; Dai, Xianzhe.

Progress in Mathematics. Vol. 271 Springer Basel, 2009. p. 1-24 (Progress in Mathematics; Vol. 271).

Research output: Chapter in Book/Report/Conference proceedingChapter

Cheeger, J & Dai, X 2009, L2-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature. in Progress in Mathematics. vol. 271, Progress in Mathematics, vol. 271, Springer Basel, pp. 1-24. https://doi.org/10.1007/978-0-8176-4743-8_1
Cheeger J, Dai X. L2-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature. In Progress in Mathematics. Vol. 271. Springer Basel. 2009. p. 1-24. (Progress in Mathematics). https://doi.org/10.1007/978-0-8176-4743-8_1
Cheeger, Jeff ; Dai, Xianzhe. / L2-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature. Progress in Mathematics. Vol. 271 Springer Basel, 2009. pp. 1-24 (Progress in Mathematics).
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