Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 6 (2015), 3155-3213.
Floer homology and splicing knot complements
We obtain a formula for the Heegaard Floer homology (hat theory) of the three-manifold obtained by splicing the complements of the knots , , in terms of the knot Floer homology of and . We also present a few applications. If denotes the rank of the Heegaard Floer group for the knot obtained by –surgery over , we show that the rank of is bounded below by
We also show that if splicing the complement of a knot with the trefoil complements gives a homology sphere –space, then is trivial and is a homology sphere –space.
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3155-3213.
Received: 4 November 2013
Revised: 19 February 2015
Accepted: 1 March 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Eftekhary, Eaman. Floer homology and splicing knot complements. Algebr. Geom. Topol. 15 (2015), no. 6, 3155--3213. doi:10.2140/agt.2015.15.3155. https://projecteuclid.org/euclid.agt/1510841064