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A short proof that the $L^p$–diameter of $\operatorname{Diff}_0(S,\mathrm{area})$ is infinite

Michał Marcinkowski

Algebraic & Geometric Topology 23 (2023) 883–893
Abstract

We give a short proof that the Lp–diameter of the group of area preserving diffeomorphisms isotopic to the identity of a compact surface is infinite.

Keywords
$L^p$ norm, diffeomorphism, Shnirelman conjecture, measure preserving diffeomorphism, braid group
Mathematical Subject Classification
Primary: 37E30, 57K10, 58D05
References
Publication
Received: 29 April 2021
Revised: 15 October 2021
Accepted: 20 November 2021
Published: 9 May 2023
Authors
Michał Marcinkowski
Institute of Mathematics
University of Wrocław
Wrocław
Poland

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