Geometry & Topology

Homotopy type of symplectomorphism groups of $S^2{\times}S^2$

Silvia Anjos

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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.

Article information

Geom. Topol., Volume 6, Number 1 (2002), 195-218.

Received: 1 October 2001
Revised: 11 March 2002
Accepted: 26 April 2002
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms 57R17: Symplectic and contact topology
Secondary: 57T20: Homotopy groups of topological groups and homogeneous spaces 57T25: Homology and cohomology of H-spaces

symplectomorphism group Pontryagin ring homotopy equivalence


Anjos, Silvia. Homotopy type of symplectomorphism groups of $S^2{\times}S^2$. Geom. Topol. 6 (2002), no. 1, 195--218. doi:10.2140/gt.2002.6.195.

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