Whitehead doubling persists

Instantons, concordance, and Whitehead doubling

We use moduli spaces of instantons and Chern-Simons invariants of flat connections to prove that the Whitehead doubles of (2,2^n-1) torus knots are independent in the smooth knot concordance group; that is, they freely generate a subgroup of infinite rank.

由怀特海德加倍产生的不可嵌入可缩开流形

Nonembeddable contractible open manifolds arising from Whitehead doubling

本文研究由非平凡纽结与半扭转迭代怀特海德加倍构造的可缩开流形，证明其不可嵌入特定度量空间，完成分类并给出完全不变量，方法可推广至高维情形。

Knot doubling operators and bordered Heegaard Floer homology

We use bordered Heegaard Floer homology to compute the tau invariant of a family of satellite knots obtained via twisted infection along two components of the Borromean rings, a generalization of Whitehead doubling. We show that tau of the resulting knot depends only on the two twisting parameters and the values of tau for the two companion knots. We also include some notes on bordered Heegaard Floer homology that may serve as a useful introduction to the subject.

加倍圆盘与卫星曲面

Doubled Disks and Satellite Surfaces

本文研究切片圆盘的正怀特黑德加倍与光滑同位素的关系，证明多种同调阻碍在卫星操作下保持，并据此构造出四维球中大量奇异圆盘及首个两两奇异切片圆盘的无限族。

JSJ-decompositions of knot and link complements in the 3-sphere

This paper is a survey of some of the most elementary consequences of the JSJ-decomposition and geometrization for knot and link complements in the 3-sphere. Formulated in the language of graphs, the result is the construction of a bijective correspondence between the isotopy classes of links in $S^3$ and a class of vertex-labelled, finite acyclic graphs, called companionship graphs. This construction can be thought of as a uniqueness theorem for Schubert's `satellite operations.' We identify precisely which graphs are companionship graphs of knots and links respectively. We also describe how …