Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms
Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms
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变形哈密顿弗洛尔理论、容量估计和卡拉比拟同构
DOI：
10.2140/gt.2011.15.1313
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发表时间：
2010
影响因子：
2
通讯作者：
Michael Usher
中科院分区：
文献类型：
--
作者：
Michael Usher
我们在辛流形的哈密顿Floer复形上发展了一族微分和裤子乘积的形变.M；！/，当传递到同调时，产生与M的大量子同调的环同构.通过研究得到的形变的oh-Schwarz谱不变量的性质，我们得到了当M具有两点约束的非零Gromov-Witten不变量时Lu的一个结果的Floer理论解释，该结果限定了M的Hofer-Zehnder容量，并给出了一个新的代数判据.当M具有Dubrovin和Manin所考虑的一般意义下的半单量子同调时(这包括所有紧环M)，以及当M是任意闭辛流形的点爆破时，后一个准则被发现是成立的。
We develop a family of deformations of the differential and of the pair-of-pants product on the Hamiltonian Floer complex of a symplectic manifold .M;!/ which upon passing to homology yields ring isomorphisms with the big quantum homology of M . By studying the properties of the resulting deformed version of the Oh‐ Schwarz spectral invariants, we obtain a Floer-theoretic interpretation of a result of Lu which bounds the Hofer‐Zehnder capacity of M when M has a nonzero Gromov‐ Witten invariant with two point constraints, and we produce a new algebraic criterion for .M;!/ to admit a Calabi quasimorphism and a symplectic quasistate. This latter criterion is found to hold whenever M has generically semisimple quantum homology in the sense considered by Dubrovin and Manin (this includes all compact toric M ), and also whenever M is a point blowup of an arbitrary closed symplectic manifold.