Covering spaces and Q-gradings on Heegaard Floer homology

Dan A. Lee; Robert Lipshitz

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Covering spaces and Q-gradings on Heegaard Floer homology

Dan A. Lee·Robert Lipshitz

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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 Spin^c 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 \bigoplus_{t\in Spin^c(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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Dan A. Lee, Robert Lipshitz. 2008-05-23. Covering spaces and Q-gradings on Heegaard Floer homology. https://arxiv.org/abs/math/0608001

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