Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
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Pin(2)-等变Seiberg-Witten Floer同调和三角剖分猜想
DOI：
10.1090/jams829
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Ciprian Manolescu
中科院分区：
文献类型：
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作者：
Ciprian Manolescu
对于具有自旋结构的有理同调3-球面，我们定义了Pin（2）-等变Seiberg-Witten Floer同调.模拟Froyshov的校正项在这种设置是一个整数值不变的同调配边，其模2减少是Rokhlin不变。作为应用，我们证明了不存在Rokhlin不变的同调3-球面Y使得Y # Y限定一个非循环光滑4-流形.根据Galewski-Stern和Matumoto以前的工作，这意味着存在不可三角化的高维流形。
We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Froyshov's correction term in this setting is an integer-valued invariant of homology cobordism whose mod 2 reduction is the Rokhlin invariant. As an application, we show that there are no homology 3-spheres Y of Rokhlin invariant one such that Y # Y bounds an acyclic smooth 4-manifold. By previous work of Galewski-Stern and Matumoto, this implies the existence of non-triangulable high-dimensional manifolds.