Khovanov module and the detection of unlinks
Geometric Topology
2014-11-11 v2 Quantum Algebra
Symplectic Geometry
Abstract
We study a module structure on Khovanov homology, which we show is natural under the Ozsvath-Szabo spectral sequence to the Floer homology of the branched double cover. As an application, we show that this module structure detects trivial links. A key ingredient of our proof is that the H_1/Torsion module structure on Heegaard Floer homology detects S^1xS^2 connected summands.
Keywords
Cite
@article{arxiv.1204.0960,
title = {Khovanov module and the detection of unlinks},
author = {Matthew Hedden and Yi Ni},
journal= {arXiv preprint arXiv:1204.0960},
year = {2014}
}
Comments
47 pages, 4 figures; Corrected error in the proof that the Khovanov module is a link invariant; Added details on homological cancellation in the presence of a filtration; Introduction revised; Typos and minor errors corrected