Homotopy type of symplectomorphism groups of S^2 X S^2
Symplectic Geometry
2014-11-11 v2
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
Cite
@article{arxiv.math/0009220,
title = {Homotopy type of symplectomorphism groups of S^2 X S^2},
author = {Silvia Anjos},
journal= {arXiv preprint arXiv:math/0009220},
year = {2014}
}
Comments
Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper7.abs.html