Surgery, polygons and SU(N)‐Floer homology
Surgery, polygons and SU(N)‐Floer homology
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手术、多边形和 SU(N)—Floer 同源性
DOI：
10.1112/topo.12137
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发表时间：
2020
影响因子：
1.1
通讯作者：
Xie, Yi
中科院分区：
文献类型：
--
作者：
Culler, Lucas;Daemi, Aliakbar;Xie, Yi
各种三维流形Floer同调理论中的外科精确三角形为研究和计算相关的Floer同调群提供了重要的工具。这些精确的三角形与三维流形的不变量有关，这些不变量是在一个固定纽结上通过三种不同的Dehn运算得到的。本文研究了关于Dehn手术的-瞬子-Floer同调的行为。特别地，证明了对于Floer同调和瞬时Floer同调，分别存在外科精确四边形和五边形。还推测-瞬子-Floer同调在一般情况下承认一个外科精确正方形。证明的一个基本步骤是在类型的ALE空间上构造一族渐近柱面度量族。这一族由维缔面体参数化，由具有正标量曲率的反自对偶度量组成。家族中的指标也承认环面对称。
Surgery exact triangles in various 3‐manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles relate the invariants of 3‐manifolds, obtained by three different Dehn surgeries on a fixed knot. In this paper, the behavior of‐instanton Floer homology with respect to Dehn surgery is studied. In particular, it is shown that there are surgery exact tetragons and pentagons, respectively, for‐ and‐instanton Floer homologies. It is also conjectured that‐instanton Floer homology in general admits a surgery exact‐gon. An essential step in the proof is the construction of a family of asymptotically cylindrical metrics on ALE spaces of type. This family is parametrized by the‐dimensional associahedron and consists of anti‐self‐dual metrics with positive scalar curvature. The metrics in the family also admit a torus symmetry.