Heegaard Floer Homology and Genus One, One Boundary Component Open Books
نویسنده
چکیده
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 T -bundle over S with first Betti number equal to one, 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 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.
منابع مشابه
Tight contact structures and genus one fibered knots
We study contact structures compatible with genus one open book decompositions with one boundary component. Any monodromy for such an open book can be written as a product of Dehn twists around dual non-separating curves in the once-punctured torus. Given such a product, we supply an algorithm to determine whether the corresponding contact structure is tight or overtwisted when the monodromy is...
متن کاملPlanar Open Books and Floer Homology
Giroux has described a correspondence between open book decompositions on a 3–manifold and contact structures. In this paper we use Heegaard Floer homology to give restrictions on contact structures which correspond to open book decompositions with planar pages, generalizing a recent result of Etnyre.
متن کاملCombinatorial Cobordism Maps in Hat Heegaard Floer Theory
In a previous paper, Sarkar and the third author gave a combinatorial description of the hat version of Heegaard Floer homology for three-manifolds. Given a cobordism between two connected three-manifolds, there is an induced map between their Heegaard Floer homologies. Assume that the first homology group of each boundary component surjects onto the first homology group of the cobordism (modul...
متن کاملNotes on the Heegaard-floer Link Surgery Spectral Sequence
In [8], P. Ozsváth and Z. Szabó constructed a spectral sequence computing the HeegaardFloer homology ĤF (YL) where YL is the result of surgery on a framed link, L, in Y . The terms in the E1-page of this spectral sequence are Heegaard-Floer homologies of surgeries on L for other framings derived from the original. They used this result to analyze the branched double cover of a link L ⊂ S3 where...
متن کاملHeegaard Floer correction terms and rational genus bounds
Given an element in the first homology of a rational homology 3– sphere Y , one can consider the minimal rational genus of all knots in this homology class. This defines a function Θ on H1(Y ;Z), which was introduced by Turaev as an analogue of Thurston norm. We will give a lower bound for this function using the correction terms in Heegaard Floer homology. As a corollary, we show that Floer si...
متن کامل