Covering spaces and Q-gradings on Heegaard Floer homology
Abstract
Heegaard Floer homology, first introduced by P. Ozsvath and Z. Szabo, associates to a 3-manifold Y a family of relatively graded Abelian groups HF(Y,t), indexed by Spinc structures t on Y. In the case that Y is a rational homology sphere, Ozsvath and Szabo lift the relative Z-grading to an absolute Q-grading. This induces a relative Q-grading on t∈ Spinc(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.
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