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Topology of the space of measure-preserving transformations of the circle
Boukhecham, Houssam
Ounesli, Hamza
2023
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e-ISSN
2464-8728
Abstract
In this paper we prove that the space of circle expanding maps of degree 2 preserving Lebesgue measure is an arc-connected space homeomorphic to an infinite-dimensional Lie group whose fundamental group is Z. The techniques involved in the proof are rather unexpected and lead to a formulation of a conjecture generalizing this result to higher dimensional infra-nilmanifolds.
Source
Houssam Boukhecham, Hamza Ounesli, "Topology of the space of measure-preserving transformations of the circle" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.55 (2023)", EUT Edizioni Università di Trieste, Trieste, 2023, pp. 165-171
Languages
en
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