#### Volume 6, issue 1 (2002)

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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 $\left(1,2\right]$. 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
##### Publication
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