English

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 LL-space? Hedden and Levine proved that splicing 0-framed complements of nontrivial knots never produces an LL-space. We extend this result to allow for arbitrary integer framings. We find that splicing two integer framed nontrivial knot complements only produces an LL-space if both knots are LL-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

R2 v1 2026-06-22T05:49:59.826Z