Covering spaces and Q-gradings on Heegaard Floer homology
نویسندگان
چکیده
Heegaard Floer homology, first introduced by P. Ozsváth and Z. Szabó in [OS04b], associates to a 3-manifold Y a family of relatively graded abelian groups HF (Y, t), indexed by Spin structures t on Y . In the case that Y is a rational homology sphere, Ozsváth and Szabó lift the relative Z-grading to an absolute Q-grading [OS06]. This induces a relative Q-grading on ⊕ t∈Spin(Y ) HF (Y, t). In this paper we describe an alternate construction of this relative Q-grading by studying the Heegaard Floer homology of covering spaces.
منابع مشابه
Computations of Heegaard Floer Homology: Torus Bundles, L-spaces, and Correction Terms
Computations of Heegaard Floer Homology: Torus Bundles, L-spaces, and Correction Terms
متن کاملHeegaard Floer Homology and Alternating Knots
In [23] we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y , which is closely related to the Heegaard Floer homology of Y (c.f. [21]). In this paper we investigate some properties of these knot homology groups for knots in the three-sphere. We give a combinatorial description for the generators of the chain complex and their gradings. With the help of th...
متن کامل2 7 O ct 2 00 4 ON THE HEEGAARD FLOER HOMOLOGY OF S 3 − p / q ( K )
Assume that the oriented 3-manifold M = S 3 −p/q (K) is obtained by a rational surgery (with coefficient −p/q < 0) along an algebraic knot K ⊂ S 3. We compute the Heegaard Floer homology of −M in terms of p/q and the Alexander polynomial of K.
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 کاملA Cylindrical Reformulation of Heegaard Floer Homology
1. Basic Definitions and Notation 3 2. Homotopy Preliminaries 6 3. Transversality 8 4. Index 12 4.1. First formulas for the index. 13 4.2. Determining S from A. 14 4.3. Comparison with classical Heegaard Floer homology. 21 4.4. Index for A ∈ π2(~x, ~x). 22 5. Admissibility Criteria 23 6. Orientations 26 7. Bubbling 27 8. Chain Complexes 29 8.1. Action of H1(Y,Z)/Tors 32 9. Isotopy invariance 34...
متن کامل