论文标题
无固定点的伪 - anosov同构，结式同源性和五薄薄油
Fixed-point-free pseudo-Anosov homeomorphisms, knot Floer homology and the cinquefoil
论文作者
论文摘要
考虑到任何$ s^3 $的属，双曲线，纤维纤维结的带有非零分数Dehn Twist系数，我们表明其伪-Anosov代表具有固定点。再加上鲍德温 - 赫 - 塞维克的最新工作，这证明了Floer同源性检测到Cinquefoil结$ t（2,5）$，并且cinquefoil是$ s^3 $中唯一的two l-space结。我们的结果在$ s^3 $中的循环分支覆盖物的浮动同源性，至$ \ Mathit {su}（2）$ - Abelian Dehn手术，以及Khovanov和Annular Khovanov同源性。在证明我们的固定点结果的过程中，我们描述了一小部分火车轨道清单，这些火车轨道载有所有伪-Anosov同构的同构，这是刺穿的磁盘上的大多数阶层。结果，我们在特定地层中找到了一个规范的曲目$τ$，其中包含所有伪 - anosov同构的同构$ \ Mathcal {q} _0 $在Two属上，并描述每个$ \ \ nathcal中的所有固定的pseudo-anosov ansosov ansomormormorphismphismodists $ \ \ natercal中的所有固定pseudo-anosov ansomormorphism {Q} _0 $。
Given any genus-two, hyperbolic, fibered knot in $S^3$ with nonzero fractional Dehn twist coefficient, we show that its pseudo-Anosov representative has a fixed point. Combined with recent work of Baldwin--Hu--Sivek, this proves that knot Floer homology detects the cinquefoil knot $T(2,5)$, and that the cinquefoil is the only genus-two L-space knot in $S^3$. Our results have applications to Floer homology of cyclic branched covers over knots in $S^3$, to $\mathit{SU}(2)$-abelian Dehn surgeries, and to Khovanov and annular Khovanov homology. Along the way to proving our fixed point result, we describe a small list of train tracks carrying all pseudo-Anosov homeomorphisms in most strata on the punctured disk. As a consequence, we find a canonical track $τ$ carrying all pseudo-Anosov homeomorphisms in a particular stratum $\mathcal{Q}_0$ on the genus-two surface, and describe every fixed-point-free pseudo-Anosov homeomorphism in $\mathcal{Q}_0$.
