Heegaard Floer homology of Matsumoto's manifolds
Heegaard Floer homology of Matsumoto's manifolds
复制标题
松本流形的 Heegaard Floer 同调
DOI：
10.1016/j.aim.2017.08.013
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发表时间：
2017
影响因子：
1.7
通讯作者：
Motoo Tange
中科院分区：
文献类型：
--
作者：
Motoo Tange;Motoo Tange
考虑由两个纽结K1，K2表示的同调球面Mn（K1，K2），纽结K1，K2的连接数为1，框架为（0，n）.我们称这个流形为松本流形。我们证明了Mn（T2，3，K2）在n< 2 τ（K2）成立的情况下，不存在任何可收缩的四维流形.给出了约化滤子的欧拉数之和的Ozsvath-Szabó τ-不变量公式。本文计算了环面纽结的扭曲Whitehead双偶的δ-不变量和Whitehead双偶的分支覆盖的修正项。利用Owens和Strle的阻塞证明了（2，7）-torus纽结的12-扭Whitehead二重和（3，7）-torus纽结的20-扭Whitehead二重不是切片，而是有界有理同调4-球的双分支覆盖.这些都是新的例子，有一个差距之间的一个结是切片和什么双分支覆盖界定一个合理的同源4球。
We consider a homology sphere M n (K 1, K 2) presented by two knots K 1, K 2 with linking number 1 and framing (0, n). We call the manifold Matsumoto's manifold. We show that M n (T 2, 3, K 2) never bounds any contractible 4-manifold if n< 2 τ (K 2) holds. We also give a formula of Ozsváth–Szabó's τ-invariant as the total sum of the Euler numbers of the reduced filtration. We compute the δ-invariants of the twisted Whitehead doubles of torus knots and correction terms of the branched covers of the Whitehead doubles. By using Owens and Strle's obstruction we show that the 12-twisted Whitehead double of the (2, 7)-torus knot and the 20-twisted Whitehead double of the (3, 7)-torus knot are not slice but the double branched covers bound rational homology 4-balls. These are new examples having a gap between what a knot is slice and what a double branched cover bounds a rational homology 4-ball.