Translator Disclaimer
2019 Kauffman states and Heegaard diagrams for tangles
Claudius Bodo Zibrowius
Algebr. Geom. Topol. 19(5): 2233-2282 (2019). DOI: 10.2140/agt.2019.19.2233

Abstract

We define polynomial tangle invariants Ts via Kauffman states and Alexander codes and investigate some of their properties. In particular, we prove symmetry relations for Ts of 4–ended tangles and deduce that the multivariable Alexander polynomial is invariant under Conway mutation. The invariants Ts can be interpreted naturally via Heegaard diagrams for tangles. This leads to a categorified version of Ts: a Heegaard Floer homology HFT̂ for tangles, which we define as a bordered sutured invariant. We discuss a bigrading on HFT̂ and prove symmetry relations for HFT̂ of 4–ended tangles that echo those for Ts.

Citation

Download Citation

Claudius Bodo Zibrowius. "Kauffman states and Heegaard diagrams for tangles." Algebr. Geom. Topol. 19 (5) 2233 - 2282, 2019. https://doi.org/10.2140/agt.2019.19.2233

Information

Received: 15 October 2017; Revised: 2 August 2018; Accepted: 6 September 2018; Published: 2019
First available in Project Euclid: 26 October 2019

zbMATH: 07142607
MathSciNet: MR4023317
Digital Object Identifier: 10.2140/agt.2019.19.2233

Subjects:
Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
50 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.19 • No. 5 • 2019
MSP
Back to Top