Symplectic automorphisms of T^*S²

1998/03/19 by Paul Seidel, Seidel, Paul · 1 citation
Mathematics · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.math/9803084

4pages, LaTex2e with xy-pic

arxiv created 1998/03/19 · arxiv updated 2009/11/30

Abstract

Let M be the cotangent bundle of S², with the standard symplectic structure. By adapting an argument of Gromov we determine the weak homotopy type of the group S of those symplectic automorphisms of M which are trivial at infinity. It turns out that S is weakly homotopy equivalent to \Z. π₀(S) is generated by the class of the standard "generalized Dehn twist". As a consequence, we show that there are different connected components of S which lie in the same connected component of the corresponding group of diffeomorphisms.

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• Slow entropy and symplectomorphisms of cotangent bundles

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