Using secondary Upsilon invariants to rule out stable equivalence of knot complexes

Allen, Samantha

doi:10.2140/agt.2020.20.29

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

Using secondary Upsilon invariants to rule out stable equivalence of knot complexes

Samantha Allen

Algebraic & Geometric Topology 20 (2020) 29–48

DOI: 10.2140/agt.2020.20.29

Abstract

Two Heegaard Floer knot complexes are called stably equivalent if an acyclic complex can be added to each complex to make them filtered chain homotopy equivalent. Hom showed that if two knots are concordant, then their knot complexes are stably equivalent. Invariants of stable equivalence include the concordance invariants $τ$ , $𝜀$ and $ϒ$ . Feller and Krcatovich gave a relationship between the Upsilon invariants of torus knots. We use secondary Upsilon invariants, defined by Kim and Livingston, to show that these relations do not extend to stable equivalence.

PDF Access Denied

We have not been able to recognize your IP address 3.15.10.137 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

stable equivalence, Upsilon, torus knot

Mathematical Subject Classification 2010

Primary: 57M25

References

Publication

Received: 10 July 2017

Accepted: 4 June 2019

Published: 23 February 2020

Authors

Samantha Allen
Department of Mathematics Dartmouth College Hanover, NH United States

Volume 20, issue 1 (2020)