论文标题
扩展排名的卫星，Whitehead双打和Heegaard Floer同源
Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology
论文作者
论文摘要
我们表明，一大批卫星运营商正在扩大排名。也就是说，它们将协和组的一些排名一组映射到无限的线性独立集上。我们的工作构成了文献中对这一属性的首次系统研究，并部分肯定了第二作者和Pinzón-Caicedo的猜想。更普遍地，我们为一个伴侣结的家族建立了一个浮动理论条件，可以在此类的卫星下具有无限级图像。我们使用的方法适合于在拓扑和一致性中琐碎起作用的模式，并且能够处理各种各样的伴侣。例如，我们给出了一个无限独立的怀特黑德双打家族，其伴侣结都具有负$τ$ -Invariant。我们的结果还恢复并扩展了使用Instanton Floer同源性建立的该领域的几个定理。
We show that a large class of satellite operators are rank-expanding; that is, they map some rank-one subgroup of the concordance group onto an infinite linearly independent set. Our work constitutes the first systematic study of this property in the literature and partially affirms a conjecture of the second author and Pinzón-Caicedo. More generally, we establish a Floer-theoretic condition for a family of companion knots to have infinite-rank image under satellites from this class. The methods we use are amenable to patterns which act trivially in topological concordance and are capable of handling a surprisingly wide variety of companions. For instance, we give an infinite linearly independent family of Whitehead doubles whose companion knots all have negative $τ$-invariant. Our also results recover and extend several theorems in this area established using instanton Floer homology.
