A filtered mapping cone formula for cables of the knot meridian

Hugo Zhou

A filtered mapping cone formula for cables of the knot meridian

Geometric Topology 2022-09-15 v1

Authors: Hugo Zhou

Abstract

We construct a filtered mapping cone formula that computes the knot Floer complex of the $(n,1)$ --cable of the knot meridian in any rational surgery, generalizing Truong's result about the $(n,1)$ --cable of the knot meridian in large surgery and Hedden-Levine's filtered mapping cone formula. As an application, we show that there exist knots in integer homology spheres with arbitrary $\varphi_{i,j}$ values for any $i>j\geq 0$ , where $\varphi_{i,j}$ are the concordance homomorphisms defined by Dai-Hom-Stoffregen-Truong.

Keywords

knot floer complex filtered mapping cone cable of knot meridian rational surgery concordance homomorphisms

Cite

@article{arxiv.2208.11289,
  title  = {A filtered mapping cone formula for cables of the knot meridian},
  author = {Hugo Zhou},
  journal= {arXiv preprint arXiv:2208.11289},
  year   = {2022}
}

Comments

Our construction follows closely the framework outlined in arXiv:1901.02488 by Hedden-Levine. 78 pages, 12 figures

A filtered mapping cone formula for cables of the knot meridian

Abstract

Keywords

Cite

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