$S^1$-equivariant symplectic homology and linearized contact homology
$S^1$-equivariant symplectic homology and linearized contact homology
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$S^1$-等变辛同调和线性化接触同调
DOI：
10.1093/imrn/rnw029
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A. Oancea
中科院分区：
文献类型：
--
作者：
F. Bourgeois;A. Oancea
给出了S^1等变辛同调的三个等价定义.我们证明了，使用有理系数，$S^1$-等变辛同调的正部分同构于线性化接触同调，当后者被定义时。我们提出了几个计算和应用，并介绍了一个严格定义的替代圆柱/线性接触的同源性的基础上的$S^1$-等变建设。
We present three equivalent definitions of $S^1$-equivariant symplectic homology. We show that, using rational coefficients, the positive part of $S^1$-equivariant symplectic homology is isomorphic to linearized contact homology, when the latter is defined. We present several computations and applications, and introduce a rigorously defined substitute for cylindrical/linearized contact homology based on an $S^1$-equivariant construction.