Geometry & Topology, Vol. 6 (2002)
Paper no. 7, pages 195--218.
Homotopy type of symplectomorphism groups of S^2 X S^2
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.
Symplectomorphism group, Pontryagin ring, homotopy equivalence
AMS subject classification.
Primary: 57S05, 57R17.
Secondary: 57T20, 57T25.
Submitted to GT on 1 October 2001.
(Revised 11 March 2002.)
Paper accepted 26 April 2002.
Paper published 27 April 2002.
Notes on file formats
Departamento de Matematica
Instituto Superior Tecnico, Lisbon, Portugal
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