Paper published by Geometry and Topology

The following paper has been published:

Geometry and Topology, Volume 9 (2005) Paper no. 21, pages 935--970

URL:
http://www.maths.warwick.ac.uk/gt/GTVol9/paper21.abs.html

Title:
Symplectomorphism groups and isotropic skeletons

Author(s):
Joseph Coffey

Abstract:

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.

AMS Classification Numbers. Primary: 57R17
Secondary: 53D35

Keywords:
Lagrangian, symplectomorphism, homotopy

Received: 25 June 2004
Revised: 24 September 2004
Accepted: 18 January 2005
Published: 25 May 2005

Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Tomasz Mrowka

Author(s) address(es):
Courant Institute for the Mathematical Sciences, New York University
251 Mercer Street, New York, NY 10012, USA
Email: coffey@xxxxxxxxxxxx

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