Splicing integer framed knot complements and bordered Heegaard Floer homology
Geometric Topology
2014-09-08 v1
Abstract
We consider the following question: when is the manifold obtained by gluing together two knot complements an -space? Hedden and Levine proved that splicing 0-framed complements of nontrivial knots never produces an -space. We extend this result to allow for arbitrary integer framings. We find that splicing two integer framed nontrivial knot complements only produces an -space if both knots are -space knots and the framings lie in an appropriate range. The proof involves a careful analysis of the bordered Heegaard Floer invariants of each knot complement.
Cite
@article{arxiv.1409.1912,
title = {Splicing integer framed knot complements and bordered Heegaard Floer homology},
author = {Jonathan Hanselman},
journal= {arXiv preprint arXiv:1409.1912},
year = {2014}
}
Comments
24 pages, 5 figures, 4 tables