no. G11
Article de recherche - Géométrie et Topologie
A note on homotopy and pseudoisotopy of diffeomorphisms of 4-manifolds
[Une note sur l’homotopie et la pseudoisotopie des diffeomorphismes des 4-variétés]
Krannich, Manuel1  ; Kupers, Alexander2
1Department of Mathematics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
2Department of Computer and Mathematical Sciences, University of Toronto Scarborough, 1265 Military Trail, Toronto, ON M1C 1A4, Canada
Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1515-1520

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.

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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

Krannich, Manuel  1   ; Kupers, Alexander  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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Krannich, Manuel; Kupers, Alexander. A note on homotopy and pseudoisotopy of diffeomorphisms of $4$-manifolds. Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1515-1520. doi: 10.5802/crmath.663

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