The symplectomorphism group of a blow up
The symplectomorphism group of a blow up
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DOI：
10.1007/s10711-007-9175-3
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发表时间：
2006-10
影响因子：
0.5
通讯作者：
D. Mcduff
中科院分区：
文献类型：
--
作者：
D. Mcduff
We study the relation between the symplectomorphism group SympMof a closed connected symplectic manifoldMand the symplectomorphism and diffeomorphism groups Sympand Diffof its one point blow up. There are three main arguments. The first shows that for any orientedMthe natural map fromtois often injective. The second argument applies whenMis simply connected and detects nontrivial elements in the homotopy groupthat persist into the space of self-homotopy equivalences of. Since it uses purely homological arguments, it applies toc-symplectic manifolds (M,a), that is, to manifolds of dimension 2nthat support a classsuch that. The third argument uses the symplectic structure onMand detects nontrivial elements in the (higher) homology ofBSymp,Musing characteristic classes defined by parametric Gromov–Witten invariants. Some results about many point blow ups are also obtained. For example we show that ifMis the four-torus withk-fold blow up(wherek> 0) thenis not generated by the groupsasranges over the set of all symplectic forms on.
