An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields
Symplectic Geometry
2013-06-19 v2 Geometric Topology
Abstract
For a closed oriented 3-manifold Y, we define an absolute grading on the Heegaard Floer homology groups of Y by homotopy classes of oriented 2-plane fields. We show that this absolute grading refines the relative one and that it is compatible with the maps induced by cobordisms. We also prove that if {\xi} is a contact structure on Y, then the grading of the contact invariant c({\xi}) is the homotopy class of {\xi}.
Keywords
Cite
@article{arxiv.1112.0290,
title = {An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields},
author = {Vinicius Gripp Barros Ramos and Yang Huang},
journal= {arXiv preprint arXiv:1112.0290},
year = {2013}
}
Comments
28 pages; added an application