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 . 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.
Citation
Silvia Anjos. "Homotopy type of symplectomorphism groups of $S^2{\times}S^2$." Geom. Topol. 6 (1) 195 - 218, 2002. https://doi.org/10.2140/gt.2002.6.195
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