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Homotopy type of symplectomorphism groups of $S^2{\times}S^2$

Silvia Anjos

Geometry & Topology 6 (2002) 195–218

arXiv: math.SG/0009220

Abstract

In this paper we discuss the topology of the symplectomorphism group of a product of two 2–dimensional spheres when the ratio of their areas lies in the interval (1,2]. More precisely we compute the homotopy type of this symplectomorphism group and we also show that the group contains two finite dimensional Lie groups generating the homotopy. A key step in this work is to calculate the mod 2 homology of the group of symplectomorphisms. Although this homology has a finite number of generators with respect to the Pontryagin product, it is unexpected large containing in particular a free noncommutative ring with 3 generators.

Keywords
symplectomorphism group, Pontryagin ring, homotopy equivalence
Mathematical Subject Classification 2000
Primary: 57S05, 57R17
Secondary: 57T20, 57T25
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Publication
Received: 1 October 2001
Revised: 11 March 2002
Accepted: 26 April 2002
Published: 27 April 2002
Proposed: Yasha Eliashberg
Seconded: Tomasz Mrowka, John Morgan
Authors
Silvia Anjos
Departamento de Matemática
Instituto Superior Técnico
Lisbon
Portugal