# Fixed point sets of isotopies on surfaces Article - 2019

Francois Beguin, Sylvain Crovisier, Frederic Le Roux

Francois Beguin, Sylvain Crovisier, Frederic Le Roux, « Fixed point sets of isotopies on surfaces  », Journal of the European Mathematical Society, à paraître

Abstract

We consider a self-homeomorphism h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F. 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 two dimensional sphere that preserves the orientation and pointwise fix some given closed connected set F.