Geometry & Topology
- Geom. Topol.
- Volume 9, Number 2 (2005), 935-970.
Symplectomorphism groups and isotropic skeletons
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 into a disjoint union of an isotropic 2–complex and a disc bundle over a symplectic surface which is Poincare dual to a multiple of the form . We show that then one can recover the homotopy type of the symplectomorphism group of from the orbit of the pair . This allows us to compute the homotopy type of certain spaces of Lagrangian submanifolds, for example the space of Lagrangian isotopic to the standard one.
Geom. Topol., Volume 9, Number 2 (2005), 935-970.
Received: 25 June 2004
Revised: 24 September 2004
Accepted: 18 January 2005
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R17: Symplectic and contact topology
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]
Coffey, Joseph. Symplectomorphism groups and isotropic skeletons. Geom. Topol. 9 (2005), no. 2, 935--970. doi:10.2140/gt.2005.9.935. https://projecteuclid.org/euclid.gt/1513799608