The symplectomorphism group of a blow up
| dc.creator | McDuff, Dusa | |
| dc.date | 2006-10-04 | |
| dc.date | 2007-07-28 | |
| dc.date.accessioned | 2026-07-07T08:20:48Z | |
| dc.date.available | 2026-07-07T08:20:48Z | |
| dc.description | We study the relation between the symplectomorphism group Symp M of a closed connected symplectic manifold M and the symplectomorphism and diffeomorphism groups Symp \TM and Diff \TM of its one point blow up \TM. There are three main arguments. The first shows that for any oriented M the natural map from pi_1(M) to pi_0(Diff \TM) is often injective. The second argument applies when M is simply connected and detects nontrivial elements in the homotopy group pi_1(Diff \TM) that persist into the space of self homotopy equivalences of \TM. Since it uses purely homological arguments, it applies to c-symplectic manifolds (M,a), that is, to manifolds of dimension 2n that support a class a in H^2(M;R) such that a^n\ne 0. The third argument uses the symplectic structure on M and detects nontrivial elements in the (higher) homology of BSymp \TM using characteristic classes defined by parametric Gromov--Witten invariants. Some results about many point blow ups are also obtained. For example we show that if M is the 4-torus with k-fold blow up \TM_k (where k>0) then pi_1(Diff \TM_k) is not generated by the groups pi_1\Symp (\TM_k, \Tom) as \Tom ranges over the set of all symplectic forms on \TM_k. | |
| dc.description | 29 pages; v3 with minor revisions, to be published in Geom. Dedicata | |
| dc.identifier | https://arxiv.org/abs/math/0610142 | |
| dc.identifier | http://arxiv.org/abs/math/0610142 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135175 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 53D35, 57R17, 57S05 | |
| dc.title | The symplectomorphism group of a blow up | |
| dc.type | text |