Heegaard Floer homology and genus one, one‐boundary component open books
By John A. Baldwin. 2008
62 citations recorded by the source corpus.
We compute the Heegaard Floer homology of any rational homology 3‐sphere with an open book decomposition of the form (T, ϕ), where T is a genus one surface with one‐boundary component. In addition, we compute the Heegaard Floer homology of every T2‐bundle over S1 with first Betti number equal to 1, and we compare our results with those of Lebow on the embedded contact homology of such torus bundles. We use these computations to place restrictions on Stein‐fillings of the contact structures compatible with such open books, to narrow down somewhat the class of 3‐braid knots with finite concordance order, and to identify all quasi‐alternating links with braid index at most 3.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3f0fc0a19c713c18e8e9368606aef56737d4319c
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the spectral sequence from Khovanov homology to Heegaard Floer homology (2008, background): “ding bi-grading (the numbers on the vertical and horizontal axes are the homological and quantum gradings, respectively). In the grid on the left, a diamond is meant to depict a generator of gKh(L′ 0)[0,1], while a star represents a generator of Khg(L′ 1)[5,14]. Since the homology of the complex f: ”
- Homologically thin, non-quasi-alternating links (2009, background): “onaldson’s celebrated “Theorem A”, which asserts that the intersection pairing of a smooth, closed, negative definite 4-manifold is diagonalizable [4]. Coupled with calculations by several researchers [1, 3, 10, 17, 30, 33], we identify 11n50 as the only knot with up to 11 crossings which is neither ”