Odd Khovanov homology

By Peter S. Ozsv'ath, Jacob Rasmussen, Zolt'an Szab'o. 2007

117 citations recorded by the source corpus.

We describe an invariant of links in the three-sphere 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 the rationals. There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones polynomial.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/99a8b241eac093078e69d3c7af31e78b8c38250a

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, background): “9Although [61] deals with odd Khovanov homology, Lemma 2.”
The Odd nilHecke Algebra and its Diagrammatics (2011, unknown): “houldplayanequallyimportant role in Khovanov homology. Surprisingly, the categoriﬁcation of the Jones polynomial is not unique. Ozsva´th, Rasmussen, and Szabo´ found anoddanalogueof Khovanov homology [14]. This odd homology theory for links agrees with the original Khovanov homology modulo 2. Both o”
Khovanov homology from Floer cohomology (2015, background): “ 1⊗x+x⊗1. The fact that one only encounters terms of the shape 1⊗x+x⊗1, and not 1⊗x−x⊗1, is the key feature which distinguishes Khovanov homology from its sign-twisted sibling “odd Khovanov” homology [37]. The symplectic arc algebra is built, as a graded vector space, out of Floer cohomology groups ”