A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds

Manuel Krannich; Alexander Kupers

doi:10.5802/crmath.663

Research article - Geometry and Topology

A note on homotopy and pseudoisotopy of diffeomorphisms of

4

-manifolds

Manuel Krannich ¹ ; Alexander Kupers ²

¹ Department of Mathematics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
² Department of Computer and Mathematical Sciences, University of Toronto Scarborough, 1265 Military Trail, Toronto, ON M1C 1A4, Canada

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1515-1520.

Abstract
Résumé

This note serves to record examples of diffeomorphisms of closed smooth $4$ -manifolds $X$ that are homotopic but not pseudoisotopic to the identity, and to explain why there are no such examples when $X$ is orientable and its fundamental group is a free group.

Cette note a pour but de présenter des exemples de diffeomorphismes d’une 4-variété lisse X qui sont homotopes mais pas pseudo-isotopes à l’identité, et d’expliquer pourquoi de tels exemples n’existent pas quand X est orientable de groupe fondamental libre.

Received: 2024-02-23
Revised: 2024-06-19
Accepted: 2024-07-07
Published online: 2024-11-14

DOI: 10.5802/crmath.663

Classification: 57R52, 57R67, 57K40
Keywords: 4-Manifolds, diffeomorphisms, pseudoisotopy, homotopy, surgery theory
Mots-clés : variété de dimension 4, difféomorphisme, homotopie, chirurgie

Author's affiliations:

Manuel Krannich ¹; Alexander Kupers ²

¹ Department of Mathematics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
² Department of Computer and Mathematical Sciences, University of Toronto Scarborough, 1265 Military Trail, Toronto, ON M1C 1A4, Canada

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds},
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     pages = {1515--1520},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2024},
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     language = {en},
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Manuel Krannich; Alexander Kupers. A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1515-1520. doi : 10.5802/crmath.663. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.663/

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