A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture
A Morse-Bott Approach to Monopole Floer
Homology and the Triangulation Conjecture
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单极子Floer同调和三角剖分猜想的Morse-Bott方法
DOI：
10.1090/memo/1221
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Francesco Lin
中科院分区：
文献类型：
--
作者：
Francesco Lin
本文将Kronheimer和Mrowka的单极子Floer同源性的构造推广到具有Morse-Bott奇点的梯度流。然后重点讨论具有自旋$^c$结构同构于其共轭的三流形的特殊情况，我们在此背景下定义了Manolescu最近的$\ mathm {Pin}(2)$-等变Seiberg-Witten-Floer同构的对偶。特别是，我们提供了另一种方法来证明他对著名的三角测量猜想的反驳。
In the present work we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped with a spin$^c$ structure isomorphic to its conjugate, we define the counterpart in this context of Manolescu's recent $\mathrm{Pin}(2)$-equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture.