Grid diagrams and Manolescu's unoriented skein exact triangle for knot Floer homology
arXiv:1305.2562 · doi:10.2140/agt.2017.17.1283
Abstract
We re-derive Manolescu's unoriented skein exact triangle for knot Floer homology over F_2 combinatorially using grid diagrams, and extend it to the case with Z coefficients by sign refinements. Iteration of the triangle gives a cube of resolutions that converges to the knot Floer homology of an oriented link. Finally, we re-establish the homological sigma-thinness of quasi-alternating links.
33 pages, 17 figures, 2 tables. v2: In this version, the main theorem (Theorem 1.3) has been modified, a missing case in the proof of Lemma 3.6 has been added, the discussion in Section 5 has been restricted to over F_2, and the exposition in Section 6 has been improved. Submitted for publication. arXiv admin note: text overlap with arXiv:math/0610559 by other authors
References in corpus (6)
- Floer homology and knot complements
- Holomorphic disks and link invariants
- On the Khovanov and knot Floer homologies of quasi-alternating links
- On combinatorial link Floer homology
- A combinatorial spanning tree model for knot Floer homology
- Bordered Floer homology and the spectral sequence of a branched double cover I