Periodic Points and Topological Restriction Homology

Cary Malkiewich; Kate Ponto

doi:10.1093/imrn/rnaa174

Periodic Points and Topological Restriction Homology

Cary Malkiewich
, Kate Ponto

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We answer in the affirmative two conjectures made by Klein and Williams. First, in a range of dimensions, the equivariant Reidemeister trace defines a complete obstruction to removing n-periodic points from a self-map f. Second, this obstruction defines a class in topological restriction homology. We prove these results using duality and trace for bicategories. This allows for immediate generalizations, including a corresponding theorem for the fiberwise Reidemeister trace.

Original language	English
Pages (from-to)	2401-2459
Number of pages	59
Journal	International Mathematics Research Notices
Volume	2022
Issue number	4
DOIs	https://doi.org/10.1093/imrn/rnaa174
State	Published - Feb 1 2022

Bibliographical note

Publisher Copyright:
© 2020 The Author(s) 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].

Funding

Funders	Funder number
National Science Foundation Arctic Social Science Program	1810779

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1093/imrn/rnaa174

Cite this

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abstract = "We answer in the affirmative two conjectures made by Klein and Williams. First, in a range of dimensions, the equivariant Reidemeister trace defines a complete obstruction to removing n-periodic points from a self-map f. Second, this obstruction defines a class in topological restriction homology. We prove these results using duality and trace for bicategories. This allows for immediate generalizations, including a corresponding theorem for the fiberwise Reidemeister trace.",

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AB - We answer in the affirmative two conjectures made by Klein and Williams. First, in a range of dimensions, the equivariant Reidemeister trace defines a complete obstruction to removing n-periodic points from a self-map f. Second, this obstruction defines a class in topological restriction homology. We prove these results using duality and trace for bicategories. This allows for immediate generalizations, including a corresponding theorem for the fiberwise Reidemeister trace.

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UR - https://www.scopus.com/pages/publications/85125492931#tab=citedBy

U2 - 10.1093/imrn/rnaa174

DO - 10.1093/imrn/rnaa174

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AN - SCOPUS:85125492931

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SP - 2401

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JO - International Mathematics Research Notices

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ER -

Periodic Points and Topological Restriction Homology

Abstract

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