pith. sign in

arxiv: 1409.1912 · v1 · pith:EVQU4Z5Bnew · submitted 2014-09-05 · 🧮 math.GT

Splicing integer framed knot complements and bordered Heegaard Floer homology

classification 🧮 math.GT
keywords complementsknotspaceframedintegerknotssplicingbordered
0
0 comments X
read the original abstract

We consider the following question: when is the manifold obtained by gluing together two knot complements an $L$-space? Hedden and Levine proved that splicing 0-framed complements of nontrivial knots never produces an $L$-space. We extend this result to allow for arbitrary integer framings. We find that splicing two integer framed nontrivial knot complements only produces an $L$-space if both knots are $L$-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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.