2016/10/03 by Béguin, François, Crovisier, Sylvain, Roux, Frédéric Le · 4 citations
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1610.00686
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.