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Hyperbolic localization and Lefschetz fixed point formulas for higher-dimensional fixed point sets

2015/04/16 by Yuichi Ike, Ike, Yuichi, Yutaka Matsui +3
Computer Science · Mathematics · Physics and Astronomy · #14C17 #14C40 #32C38 #35A27 #37C25 #55N33 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.AG #msc:14C17 #msc:14C40 #msc:32C38 #msc:35A27 #msc:37C25 #msc:55N33

paper · pdf · doi:10.48550/arxiv.1504.04185

38 pages, revised. arXiv admin note: substantial text overlap with arXiv:0812.4480

openalex publication_date 2015/04/16 · arxiv created 2015/05/25 · arxiv updated 2015/05/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study Lefschetz fixed point formulas for constructible sheaves with higher-dimensional 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 in particular for smooth fixed point components. In the course of the proof, the new Lagrangian cycles introduced in our previous paper will be effectively used. Moreover we show various examples for which local contributions can be explicitly determined by our method.

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