On knot Floer homology in double branched covers
By Lawrence P. Roberts. 2007
66 citations recorded by the source corpus.
Let L be a link in an thickened annulus. We specify the embedding of this annulus in the three sphere, and consider its complement thought of as the axis to L. In the right circumstances this axis lifts to a null-homologous knot in the double branched cover of the three sphere, branched over the embedded copy of L. This paper shows that the knot Floer homology of this lift, with mod 2 coefficients, can be computed from a spectral sequence starting at a type of Khovanov homology already described by Asaeda, Przytycki, and Sikora. We extend the known results about this type of Khovanov homology, and use it to provide a very simple explanation of the case when L is alternating for the obvious projection.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ff24eac79142bc983dffbde4a77dfb45253e1c26
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A combinatorial spanning tree model for knot Floer homology (2011, background): “The isomorphism on knot Floer homology associated to an isotopy may also be defined by counting pseudo-holomorphic triangles [26, 46] (though it was not originally defined in this way).”
- Annular Khovanov homology and knotted Schur–Weyl representations (2015, methodology): “Roberts in [33], who related it to Heegaard Floer knot homology as in [27] (see Sec.”
- On the equivalence of Legendrian and transverse invariants in knot Floer homology (2011, unknown): “Roberts proves in [37] that .”
- Khovanov module and the detection of unlinks (2012, background): “Their result had numerous antecedents (see Baldwin [1], Baldwin and Levine [2], Baldwin and Plamenevskaya [3], Grigsby and Wehrli [10], the authors [11; 12], the first author and Watson [13] and Roberts [32]), most aimed at generalizing or exploiting a spectral sequence discovered by Ozsváth and Sza”
- Quantum link homology via trace functor I (2016, methodology): “W:= spank{w+,w−}, V := spank{v+,v−}, (5.13) respectively, with the degree defined on generators as degw± = ±1, degv± = 0. (5.14) This degree is denoted by j′ in [GLW15] and differs from the one used in [Rob13]. In addition, the modules admit the annular grading, denoted adeg and defined as adegw± = 0, ”