Covering spaces and Q-gradings on Heegaard Floer homology

Details Covering spaces and Q-gradings on Heegaard Floer homology Covering spaces and Q-gradings on Heegaard Floer homology

2006-07-31

arxiv.org/abs/math/0608001v2

Journal of Symplectic Geometry, Volume 6, Number 1, 2008

Mathematics

Geometric Topology

25 pages, 1 figure. Minor revisions. This version matches published version more closely

Scientific paper

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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