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arXiv · 1610.00686

Fixed point sets of isotopies on surfaces

François Béguin·Sylvain Crovisier·Frédéric Le Roux
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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.

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François Béguin, Sylvain Crovisier, Frédéric Le Roux. 2016-10-03. Fixed point sets of isotopies on surfaces. https://arxiv.org/abs/1610.00686

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