Rabinowitz-Floer homology on Brieskorn manifolds
Rabinowitz-Floer homology on Brieskorn manifolds
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Brieskorn 流形上的 Rabinowitz-Floer 同调
DOI：
10.18452/17501
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Alexander Fauck
中科院分区：
文献类型：
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作者：
Alexander Fauck
本文研究奇维流形上的可填充切触结构。为此目的，使用由Cieliebak和Frauenfelder在2009年引入的Rabinowitz-Floer同源性（RFH）。论文的主要部分是致力于RFH的定义中的技术问题。特别是，它表明，所涉及的模空间被切断横向。此外，还证明了RFH在亚临界柄连接下是本质不变的。最后，计算了某些Brieskorn流形的RFH。然后使用所获得的结果来表明，对于每个支持可填充接触结构的流形，要么存在无限多个不同的可填充接触结构，要么存在一个具有无限多个不同填充物的接触结构，或者对于每个可填充接触结构，RFH都是无限维的。度。
This thesis considers fillable contact structures on odd-dimensional manifolds. For that purpose, Rabinowitz-Floer homology (RFH) is used which was introduced by Cieliebak and Frauenfelder in 2009. A major part of the thesis is devoted to technical problems in the definition of RFH. In particular, it is shown that the moduli spaces involved are cut out transversally. Moreover, it is proved that RFH is essentially invariant under subcritical handle attachment. Finally, RFH is calculated for some Brieskorn manifolds. The obtained results are then used to show for every manifold, which supports fillable contact structures, that there exist either infinitely many different fillable contact structures, or one contact structure with infinitely many different fillings or for every fillable contact structure holds that RFH is infinite dimensional in every degree.
辛同调和 Eilenberg-Steenrod 公理
DOI：
10.2140/agt.2018.18.1953
发表时间：
1953
期刊：
arXiv: Symplectic Geometry
影响因子：
--
作者：
Cieliebak;Oancea;Alexandru
通讯作者：
Alexandru