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arXiv · 2305.03490

Topology of the space of measure-preserving transformations of the circle

Houssam Boukhecham·Hamza Ounesli
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Abstract

This paper is dedicated to 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 $\mathbb{Z}$. The techniques involved in the proof are rather unexpected and lead to a formulation of a general conjecture

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Houssam Boukhecham, Hamza Ounesli. 2023-05-05. Topology of the space of measure-preserving transformations of the circle. https://arxiv.org/abs/2305.03490

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