Fixed point sets of isotopies on surfaces
François Béguin
Université Paris 13, Villetaneuse, FranceSylvain Crovisier
Université Paris Sud, Orsay, FranceFrédéric Le Roux
Université Pierre et Marie Curie, Paris, France
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Abstract
We consider a self-homeomorphism of some surface . A subset of the fixed point set of is said to be unlinked if there is an isotopy from the identity to that fixes every point of . With Le Calvez’ transverse foliations theory in mind, we prove the existence of unlinked sets that are maximal with respect to inclusion. As a byproduct, we prove the arcwise connectedness of the space of homeomorphisms of the 2-sphere that preserve orientation and pointwise fix some given closed connected set .
Cite this article
François Béguin, Sylvain Crovisier, Frédéric Le Roux, Fixed point sets of isotopies on surfaces. J. Eur. Math. Soc. 22 (2020), no. 6, pp. 1971–2046
DOI 10.4171/JEMS/960