Geodesic
Homotopy type of symplectomorphism groups of S2×S2
Anjos, Silvia1
1 Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal
Geometry & topology, Tome 6 (2002) no. 1, pp. 195-218.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2002.6.195
Keywords: symplectomorphism group, Pontryagin ring, homotopy equivalence

Anjos, Silvia 1

1 Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal 
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     title = {Homotopy type of symplectomorphism groups of {S2{\texttimes}S2}},
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Anjos, Silvia. Homotopy type of symplectomorphism groups of S2×S2. Geometry & topology, Tome 6 (2002) no. 1, pp. 195-218. doi : 10.2140/gt.2002.6.195. http://geodesic.mathdoc.fr/articles/10.2140/gt.2002.6.195/

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