Splicing knot complements and bordered Floer homology
Geometric Topology
2015-09-11 v2 Symplectic Geometry
Abstract
We show that the integer homology sphere obtained by splicing two nontrivial knot complements in integer homology sphere L-spaces has Heegaard Floer homology rank strictly greater than one. In particular, splicing the complements of nontrivial knots in the 3-sphere never produces an L-space. The proof uses bordered Floer homology.
Keywords
Cite
@article{arxiv.1210.7055,
title = {Splicing knot complements and bordered Floer homology},
author = {Matthew Hedden and Adam Simon Levine},
journal= {arXiv preprint arXiv:1210.7055},
year = {2015}
}
Comments
25 pages. Revised version, to appear in Crelle's Journal. Errors from the original version have been corrected