Hyperbolic ocalization and Lefschetz ixed oint ormulas for igher- imensional ixed oint ets

Yuichi Ike, Yutaka Matsui, Kiyoshi Takeuchi

Research output: Contribution to journalArticlepeer-review

Abstract

We study Lefschetz fixed point formulas for constructible sheaves with higherdimensional fixed point sets. Under fairly weak assumptions, we prove that the local contributions from them are expressed by some constructible functions associated to hyperbolic localizations. This gives an affirmative answer to a conjecture of Goresky- MacPherson [8] in particular for smooth fixed point components (see [9, page 9, (1.12) Open problems]). In the course of the proof, the new Lagrangian cycles introduced in our previous article [20] will be effectively used. Moreover, we show various examples for which local contributions can be explicitly determined by our method.

Original languageEnglish
Pages (from-to)4852-4898
Number of pages47
JournalInternational Mathematics Research Notices
Volume2018
Issue number15
DOIs
Publication statusPublished - 2018 Aug 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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