Odd Khovanov homology is mutation invariant

By J. Bloom. 2009

54 citations recorded by the source corpus.

We define a link homology theory that is readily seen to be both isomorphic to reduced odd Khovanov homology and fully determined by data impervious to Conway mutation. This gives an elementary proof that odd Khovanov homology is mutation invariant, and therefore that mod 2 Khovanov homology is mutation invariant. We also establish mutation invariance for the entire Ozsvath-Szabo spectral sequence from reduced Khovanov homology to the Heegaard Floer homology of the branched double cover.

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

View Paper: https://www.semanticscholar.org/paper/16620bd1a9f792f3511f80863cb03309969c1dd1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. A. Stipsicz
2. John A. Baldwin
3. Peter S. Ozsv'ath
4. Zolt'an Szab'o
5. J. Bloom
6. A. Levine
7. Ciprian Manolescu
8. Jacob Rasmussen

In Geometry and Topology

1. John A. Baldwin
2. A. Stipsicz
3. Peter S. Ozsv'ath
4. Zolt'an Szab'o
5. J. Bloom
6. A. Levine
7. Ciprian Manolescu
8. M. Hedden

In Mathematical Physics

1. John A. Baldwin
2. A. Stipsicz
3. Peter S. Ozsv'ath
4. Zolt'an Szab'o
5. J. Bloom
6. A. Levine
7. M. Hedden
8. Ciprian Manolescu

Citations in the corpus

• Grid Homology for Knots and Links (2015, background): “Related questions can be asked for Khovanov homology; see [14, 225].”
• A combinatorial spanning tree model for knot Floer homology (2011, background): “fter a halfrotation, as in the figure below. Mutation leaves all classical link polynomials unchanged and preserves the homeomorphism type of the branched double cover. Moreover, Wehrli [56] and Bloom [3] have shown that it preserves reduced Khovanov homology (with coefficients in F). In contrast, muta”
• A link surgery spectral sequence in monopole Floer homology (2009, methodology): “slated fairly directly, we instead present a more global identication of the E1 page with the reduced Khovanov complex, based on our \thriftier" construction of the reduced odd Khovanov complex [3]. The intermediate pages are link invariants as well. Beyond these objectives, we rene the link su”
• Odd Khovanov homology (2007, unknown): “Since the first appearance of this preprint, there have been several further developments related to the constructions presented in this paper; see for example Bloom [2], Putyra [13], Shumakovitch [16] and the third author [17].”