Volume 15, issue 6 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Floer homology and splicing knot complements

Eaman Eftekhary

Algebraic & Geometric Topology 15 (2015) 3155–3213
Abstract

We obtain a formula for the Heegaard Floer homology (hat theory) of the three-manifold Y (K1,K2) obtained by splicing the complements of the knots Ki Y i, i = 1,2, in terms of the knot Floer homology of K1 and K2. We also present a few applications. If hni denotes the rank of the Heegaard Floer group HFK̂ for the knot obtained by n–surgery over Ki, we show that the rank of HF̂(Y (K1,K2)) is bounded below by

|(h1 h 11)(h 2 h 12) (h 01 h 11)(h 02 h 12)|.

We also show that if splicing the complement of a knot K Y with the trefoil complements gives a homology sphere L–space, then K is trivial and Y is a homology sphere L–space.

Keywords
Floer homology, splicing, essential torus
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R58
References
Publication
Received: 4 November 2013
Revised: 19 February 2015
Accepted: 1 March 2015
Published: 12 January 2016
Authors
Eaman Eftekhary
School of Mathematics
Institute for Research in Fundamental Sciences (IPM)
PO Box 19395-5746
Tehran 19395
Iran
http://math.ipm.ir/~eftekhary