Homotopy type of symplectomorphism groups of S2×S2

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

symplectomorphism group, Pontryagin ring, homotopy equivalence

Mathematical Subject Classification 2000

Primary: 57S05, 57R17

Secondary: 57T20, 57T25

References

Forward citations

Publication

Received: 1 October 2001

Revised: 11 March 2002

Accepted: 26 April 2002

Published: 27 April 2002

Proposed: Yasha Eliashberg

Seconded: Tomasz Mrowka, John Morgan

Authors

Silvia Anjos
Departamento de Matemática Instituto Superior Técnico Lisbon Portugal

Volume 6, issue 1 (2002)

Silvia Anjos