On the naturality of the spectral sequence from Khovanov homology to Heegaard Floer homology

Ozsvath and Szabo have established an algebraic relationship, in the form of a spectral sequence, between the reduced Khovanov homology of (the mirror of) a link L in S^3 and the Heegaard Floer homology of its double-branched cover. This relationship has since been recast by the authors as a specific instance of a broader connection between Khovanov- and Heegaard Floer-type homology theories, using a version of Heegaard Floer homology for sutured manifolds developed by Juhasz. In the present work we prove the naturality of the spectral sequence under certain elementary TQFT operations, using a generalization of Juhasz's surface decomposition theorem valid for decomposing surfaces geometrically disjoint from an imbedded framed link.Comment: 36 pages, 13 figure

On Gradings in Khovanov homology and sutured Floer homology

We discuss generalizations of Ozsvath-Szabo's spectral sequence relating Khovanov homology and Heegaard Floer homology, focusing attention on an explicit relationship between natural Z (resp., 1/2 Z) gradings appearing in the two theories. These two gradings have simple representation-theoretic (resp., geometric) interpretations, which we also review.Comment: 17 pages, 5 figures, to be submitted to Proceedings of Jaco's 70th Birthday Conference, 201

Khovanov Homology, Sutured Floer Homology, and Annular Links

Lawrence Roberts, extending the work of Ozsvath-Szabo, showed how to associate to a link, L, in the complement of a fixed unknot, B in S3, a spectral sequence from the Khovanov homology of a link in a thickened annulus to the knot Floer homology of the preimage of B inside the double-branched cover of L. In a previous paper, we extended Ozsvath-Szabo\u27s spectral sequence in a different direction, constructing for each knot K in S3 and each positive integer n, a spectral sequence from Khovanov\u27s categorification of the reduced, n-colored Jones polynomial to the sutured Floer homology of a reduced n-cable of K. In the present work, we reinterpret Roberts\u27 result in the language of Juhasz\u27s sutured Floer homology and show that our spectral sequence is a direct summand of Roberts\u27

Development of fuel cell electrodes, Electrode improvement and life testing, tasks 1 and 3 Final report, 30 Jun. 1966 - 30 Apr. 1968

Volt-ampere characteristics improvement and life testing of electrodes for hydrogen oxygen fuel cell