1. Reducible surgeries and Heegaard Floer homology
- Author
-
Jennifer Hom, Tye Lidman, and Nicholas Zufelt
- Subjects
General Mathematics ,010102 general mathematics ,Physics::Medical Physics ,Geometric Topology (math.GT) ,01 natural sciences ,Mathematics::Geometric Topology ,Combinatorics ,Mathematics - Geometric Topology ,Floer homology ,Genus (mathematics) ,0103 physical sciences ,FOS: Mathematics ,57M25, 57M27, 57R58 ,010307 mathematical physics ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics ,Knot (mathematics) - Abstract
In this paper, we use Heegaard Floer homology to study reducible surgeries. In particular, suppose K is a non-cable knot in the three-sphere with an L-space surgery. If p-surgery on K is reducible, we show that p equals 2g(K)-1. This implies that any knot with an L-space surgery has at most one reducible surgery, a fact that we show additionally for any knot of genus at most two., 15 pages, 2 figures; added an additional author and a new section (3.2) which improves Theorem 1.3
- Published
- 2013