Journal of Symplectic Geometry

Volume 15 (2017)

Number 3

Floer theory and topology of $\mathrm{Diff} (S^2)$

Pages: 853 – 859

DOI: http://dx.doi.org/10.4310/JSG.2017.v15.n3.a8

Author

Yasha Savelyev (CUICBAS, University of Colima, Mexico)

Abstract

We say that a fixed point of a diffeomorphism is non-degenerate if $1$ is not an eigenvalue of the linearization at the fixed point. We use pseudo-holomorphic curves techniques to prove the following: the inclusion map $i : \mathrm{Diff}^1 (S^2) \to \mathrm{Diff} (S^2)$ vanishes on all homotopy groups, where $\mathrm{Diff}^1 (S^2) \subset \mathrm{Diff}(S^2)$ denotes the space of orientation preserving diffeomorphisms of $S^2$ with a prescribed non-degenerate fixed point. This complements the classical results of Smale and Eels and Earl.

Keywords

Floer theory, positivity of intersections, groups of diffeomorphisms

Full Text (PDF format)

Received 20 August 2015

Published 8 September 2017