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Unoriented Khovanov Homology. / Baldridge, Scott; Kauffman, Louis H.; McCarty, Ben.

In: New York Journal of Mathematics, Vol. 28, 14, 2022, p. 367-401.

Research output: Contribution to journal › Article › peer-review

Harvard

Baldridge, S, Kauffman, LH & McCarty, B 2022, 'Unoriented Khovanov Homology', New York Journal of Mathematics, vol. 28, 14, pp. 367-401. <https://nyjm.albany.edu/j/2022/28-14v.pdf>

APA

Baldridge, S., Kauffman, L. H., & McCarty, B. (2022). Unoriented Khovanov Homology. New York Journal of Mathematics, 28, 367-401. [14]. https://nyjm.albany.edu/j/2022/28-14v.pdf

Vancouver

Baldridge S, Kauffman LH, McCarty B. Unoriented Khovanov Homology. New York Journal of Mathematics. 2022;28:367-401. 14.

Author

Baldridge, Scott ; Kauffman, Louis H. ; McCarty, Ben. / Unoriented Khovanov Homology. In: New York Journal of Mathematics. 2022 ; Vol. 28. pp. 367-401.

BibTeX

@article{72eb708fa568484da606466c5238f9c8,
title = "Unoriented Khovanov Homology",
abstract = "The Jones polynomial and Khovanov homology of a classical link are invariants that depend upon an initial choice of orientation for the link. In this paper, we give a Khovanov homology theory for unoriented virtual links. The graded Euler characteristic of this homology is proportional to a similarly-defined unoriented Jones polynomial for virtual links, which is a new invariant in the category of non-classical virtual links. The unoriented Jones polynomial continues to satisfy an important property of the usual one: for classical or even virtual links, the unoriented Jones polynomial evaluated at one is two to the power of the number of components of the link. As part of extending the main results of this paper to non-classical virtual links, a new framework for computing integral Khovanov homology based upon arc-labeled diagrams is described. This framework can be efficiently and effec-tively implemented on a computer. We define an unoriented Lee homology theory for virtual links based upon the unoriented version of Khovanov ho-mology.",
keywords = "Core, Jones polyno-mial, Khovanov homology, Knot, Lee homology, Mantle, Multicore decomposition, Parity, Unoriented, Virtual link",
author = "Scott Baldridge and Kauffman, {Louis H.} and Ben McCarty",
note = "Funding Information: Acknowledgements. Kauffman{\textquoteright}s work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (under contract number 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation). All three authors would like to thank William Rushworth for many helpful conversations and suggestions. Publisher Copyright: {\textcopyright} 2022, University at Albany. All rights reserved.",
year = "2022",
language = "English",
volume = "28",
pages = "367--401",
journal = "New York Journal of Mathematics",
issn = "1076-9803",
publisher = "Electronic Journals Project",

}

RIS

TY - JOUR

T1 - Unoriented Khovanov Homology

AU - Baldridge, Scott

AU - Kauffman, Louis H.

AU - McCarty, Ben

N1 - Funding Information: Acknowledgements. Kauffman’s work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (under contract number 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation). All three authors would like to thank William Rushworth for many helpful conversations and suggestions. Publisher Copyright: © 2022, University at Albany. All rights reserved.

PY - 2022

Y1 - 2022

N2 - The Jones polynomial and Khovanov homology of a classical link are invariants that depend upon an initial choice of orientation for the link. In this paper, we give a Khovanov homology theory for unoriented virtual links. The graded Euler characteristic of this homology is proportional to a similarly-defined unoriented Jones polynomial for virtual links, which is a new invariant in the category of non-classical virtual links. The unoriented Jones polynomial continues to satisfy an important property of the usual one: for classical or even virtual links, the unoriented Jones polynomial evaluated at one is two to the power of the number of components of the link. As part of extending the main results of this paper to non-classical virtual links, a new framework for computing integral Khovanov homology based upon arc-labeled diagrams is described. This framework can be efficiently and effec-tively implemented on a computer. We define an unoriented Lee homology theory for virtual links based upon the unoriented version of Khovanov ho-mology.

AB - The Jones polynomial and Khovanov homology of a classical link are invariants that depend upon an initial choice of orientation for the link. In this paper, we give a Khovanov homology theory for unoriented virtual links. The graded Euler characteristic of this homology is proportional to a similarly-defined unoriented Jones polynomial for virtual links, which is a new invariant in the category of non-classical virtual links. The unoriented Jones polynomial continues to satisfy an important property of the usual one: for classical or even virtual links, the unoriented Jones polynomial evaluated at one is two to the power of the number of components of the link. As part of extending the main results of this paper to non-classical virtual links, a new framework for computing integral Khovanov homology based upon arc-labeled diagrams is described. This framework can be efficiently and effec-tively implemented on a computer. We define an unoriented Lee homology theory for virtual links based upon the unoriented version of Khovanov ho-mology.

KW - Core

KW - Jones polyno-mial

KW - Khovanov homology

KW - Knot

KW - Lee homology

KW - Mantle

KW - Multicore decomposition

KW - Parity

KW - Unoriented

KW - Virtual link

UR - http://www.scopus.com/inward/record.url?scp=85124731766&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85124731766

VL - 28

SP - 367

EP - 401

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

M1 - 14

ER -

ID: 35551317