Symplectomorphism groups and isotropic skeletons

Details Symplectomorphism groups and isotropic skeletons Symplectomorphism groups and isotropic skeletons

2004-04-27

arxiv.org/abs/math/0404496v4

Geom. Topol. 9(2005) 935-970

Mathematics

Symplectic Geometry

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper21.abs.html

Scientific paper

The symplectomorphism group of a 2-dimensional surface is homotopy equivalent to the orbit of a filling system of curves. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition of the symplectic 4-manifold (M, omega) into a disjoint union of an isotropic 2-complex L and a disc bundle over a symplectic surface Sigma which is Poincare dual to a multiple of the form omega. We show that then one can recover the homotopy type of the symplectomorphism group of M from the orbit of the pair (L, Sigma). This allows us to compute the homotopy type of certain spaces of Lagrangian submanifolds, for example the space of Lagrangian RP^2 in CP^2 isotopic to the standard one.

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