论文标题
Mazur模式的作用直到拓扑结合
Action of the Mazur pattern up to topological concordance
论文作者
论文摘要
在80年代，弗里德曼（Freedman）表明，怀特黑德（Whitehead）的操作员在拓扑结构上均匀地行动。另一方面，阿克布鲁特（Akbulut）表明，怀特黑德（Whitehead）双倍的操作员在非试图方面起作用，以达到平滑的一致性。 Mazur模式是卫星操作员的自然候选者，它以拓扑结构的身份起作用，但并非平滑的一致性。最近，人们对Mazur模式的作用进行了研究，直到在平滑和拓扑类别中进行一致性。示例表明，Cochran-Franklin-Hedden-Horn和Collins给出了Mazur模式并非由身份到平滑和一致性的作用。在本文中，我们提供了证据表明，Mazur模式通过拓扑结合的身份起作用。 特别是，我们表明两个卫星操作员$ p_ {k_0，η_0} $和$ p_ {k_1，η_1} $，带有$η_0$和$η_1$自由同型在拓扑concordance集团modulo上具有相同的同型$（1）$（1）$ solvable knevable knevers conterment conterment conterment conterment contect，以使其与他们相同的套餐，以使其与他们相处。特别是，Mazur模式和身份操作员以这种方式相关，因此这是对Whitehead兼而有之的拓扑侧的证据。我们提供了其他证据，表明他们在整个拓扑协调组中采取了相同的行动，表明他们无法通过卡森 - 戈登（Casson-Gordon）签名或metabelian $ρ$ invariants来区分它们。
In the '80s, Freedman showed that the Whitehead doubling operator acts trivally up to topological concordance. On the other hand, Akbulut showed that the Whitehead doubling operator acts nontrivially up to smooth concordance. The Mazur pattern is a natural candidate for a satellite operator which acts by the identity up to topological but not smooth concordance. Recently there has been a resurgence of study of the action of the Mazur pattern up to concordance in the smooth and topological categories. Examples showing that the Mazur pattern does not act by the identity up to smooth concordance have been given by Cochran-Franklin-Hedden-Horn and Collins. In this paper, we give evidence that the Mazur pattern acts by the identity up to topological concordance. In particular, we show that two satellite operators $P_{K_0,η_0}$ and $P_{K_1,η_1}$ with $η_0$ and $η_1$ freely homotopic have the same action on the topological concordance group modulo the subgroup of $(1)$-solvable knots, which gives evidence that they act in the same way up to topological concordance. In particular, the Mazur pattern and the identity operator are related in this way, and so this is evidence for the topological side of the analogy to the Whitehead doubling operator. We give additional evidence that they have the same action on the full topological concordance group by showing that up to topological concordance they cannot be distinguished by Casson-Gordon signatures or metabelian $ρ$-invariants.
