Odd khovanov homology

Peter S. Ozsváth; Jacob Rasmussen; Zoltán Szabó

doi:10.2140/agt.2013.13.1465

Odd khovanov homology

Peter S. Ozsváth, Jacob Rasmussen, Zoltán Szabó

Mathematics

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

55 Scopus citations

Abstract

We describe an invariant of links in S³ which is closely related to Khovanov's Jones polynomial homology. Our construction replaces the symmetric algebra appearing in Khovanov's definition with an exterior algebra. The two invariants have the same reduction modulo 2, but differ over Q. There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones polynomial.

Original language	English (US)
Pages (from-to)	1465-1488
Number of pages	24
Journal	Algebraic and Geometric Topology
Volume	13
Issue number	3
DOIs	https://doi.org/10.2140/agt.2013.13.1465
State	Published - Apr 30 2013

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Homology
Khovanov
Knot
Link

Access to Document

10.2140/agt.2013.13.1465

Cite this

@article{02767d1f0b284fc99f92d674676ad834,

title = "Odd khovanov homology",

abstract = "We describe an invariant of links in S3 which is closely related to Khovanov's Jones polynomial homology. Our construction replaces the symmetric algebra appearing in Khovanov's definition with an exterior algebra. The two invariants have the same reduction modulo 2, but differ over Q. There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones polynomial.",

keywords = "Homology, Khovanov, Knot, Link",

author = "Ozsv{\'a}th, {Peter S.} and Jacob Rasmussen and Zolt{\'a}n Szab{\'o}",

year = "2013",

month = apr,

day = "30",

doi = "10.2140/agt.2013.13.1465",

language = "English (US)",

volume = "13",

pages = "1465--1488",

journal = "Algebraic and Geometric Topology",

issn = "1472-2747",

publisher = "Mathematical Sciences Publishers",

number = "3",

}

TY - JOUR

T1 - Odd khovanov homology

AU - Ozsváth, Peter S.

AU - Rasmussen, Jacob

AU - Szabó, Zoltán

PY - 2013/4/30

Y1 - 2013/4/30

N2 - We describe an invariant of links in S3 which is closely related to Khovanov's Jones polynomial homology. Our construction replaces the symmetric algebra appearing in Khovanov's definition with an exterior algebra. The two invariants have the same reduction modulo 2, but differ over Q. There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones polynomial.

AB - We describe an invariant of links in S3 which is closely related to Khovanov's Jones polynomial homology. Our construction replaces the symmetric algebra appearing in Khovanov's definition with an exterior algebra. The two invariants have the same reduction modulo 2, but differ over Q. There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones polynomial.

KW - Homology

KW - Khovanov

KW - Knot

KW - Link

UR - http://www.scopus.com/inward/record.url?scp=84877096780&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877096780&partnerID=8YFLogxK

U2 - 10.2140/agt.2013.13.1465

DO - 10.2140/agt.2013.13.1465

M3 - Article

AN - SCOPUS:84877096780

SN - 1472-2747

VL - 13

SP - 1465

EP - 1488

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 3

ER -

Odd khovanov homology

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this