Knot doubling operators and bordered Heegaard Floer homology

TL;DR

This paper employs bordered Heegaard Floer homology to compute the tau invariant of a family of satellite knots, revealing its dependence on twisting parameters and companion knots, and offers introductory notes on the subject.

Contribution

It introduces a method to compute tau invariants for twisted satellite knots using bordered Heegaard Floer homology, generalizing Whitehead doubling.

Findings

Tau depends only on twisting parameters and companion tau values.

Provides a computational framework for satellite knots.

Includes introductory notes on bordered Heegaard Floer homology.

Abstract

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.