Homotopy type of symplectomorphism groups of S^2 X S^2

Details Homotopy type of symplectomorphism groups of S^2 X S^2 Homotopy type of symplectomorphism groups of S^2 X S^2

2000-09-25

arxiv.org/abs/math/0009220v2

Geom. Topol. 6 (2002) 195-218

Mathematics

Symplectic Geometry

Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper7.abs.html

Scientific paper

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.

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