Fixed point sets of isotopies on surfaces

  • François Béguin

    Université Paris 13, Villetaneuse, France
  • Sylvain Crovisier

    Université Paris Sud, Orsay, France
  • Frédéric Le Roux

    Université Pierre et Marie Curie, Paris, France
Fixed point sets of isotopies on surfaces cover
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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