Floer theory and topology of $Diff(S^2)$

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 $$i:{\text{Diff}}^1(S^2)\to \text{Diff}(S^2)$$ vanishes on all homotopy groups, where ${\text{Diff}}^1(S^2)\subset \text{Diff}(S^2)$ 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.

Version accepted by JSG, 5pgs, contents slightly changed

References in corpus (2)

• Quantum characteristic classes and the Hofer metric
• On the injectivity radius in Hofer's geometry