### Abstract

We study from a mostly topological standpoint the L^{2}-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 L^{2}-cohomology of certain noncompact hyperkähler manifolds that admit geometrically fibered end structures.

Original language | English (US) |
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Title of host publication | Progress in Mathematics |

Publisher | Springer Basel |

Pages | 1-24 |

Number of pages | 24 |

Volume | 271 |

DOIs | |

State | Published - Jan 1 2009 |

### Publication series

Name | Progress in Mathematics |
---|---|

Volume | 271 |

ISSN (Print) | 0743-1643 |

ISSN (Electronic) | 2296-505X |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology

### Cite this

^{2}-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

**L ^{2}-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature.** / Cheeger, Jeff; Dai, Xianzhe.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

^{2}-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

^{2}-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

}

TY - CHAP

T1 - L2-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature

AU - Cheeger, Jeff

AU - Dai, Xianzhe

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85026023490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026023490&partnerID=8YFLogxK

U2 - 10.1007/978-0-8176-4743-8_1

DO - 10.1007/978-0-8176-4743-8_1

M3 - Chapter

VL - 271

T3 - Progress in Mathematics

SP - 1

EP - 24

BT - Progress in Mathematics

PB - Springer Basel

ER -