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

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arxiv 2402.16167 v3 pith:GXFQBWEM submitted 2024-02-25 math.GT math.AT

Manuel Krannich , Alexander Kupers This is my paper · ORCID
classification math.GTmath.AT
keywords diffeomorphismsexamplesgroupmanifoldsnoteclosedexplainfree
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abstract

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.

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  1. Smoothing topological pseudo-isotopies of 4-manifolds

    math.GT 2025-07 accept novelty 8.0 of 10

    The paper proves a Kirby-Siebenmann obstruction criterion for smoothing topological pseudo-isotopies of 4-manifolds, gives new positive cases for certain fundamental groups, and constructs the first diffeomorphisms th...

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