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

DOI10.4310/JSG.2017.V15.N3.A8zbMATH Open1380.53099arXiv1409.3975OpenAlexW2753340153MaRDI QIDQ1689668

Yasha Savelyev

Publication date: 17 January 2018

Published in: The Journal of Symplectic Geometry (Search for Journal in Brave)

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 ${\displaystyle }$i: ext{Diff} ^{1} (S ^{2} ) o ext{Diff} (S^2)${\displaystyle }$ vanishes on all homotopy groups, where $ext{Diff}^1(S^2)subsetextDiff(S^2)$ 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.

Full work available at URL: https://arxiv.org/abs/1409.3975

zbMATH Keywords

groups of diffeomorphismsFloer theorypositivity of intersections

Mathematics Subject Classification ID

Symplectic aspects of Floer homology and cohomology (53D40) Floer homology (57R58) Pseudoholomorphic curves (32Q65)

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