Contact structures and reducible surgeries
File(s)paper.pdf (467.71 KB)
Accepted version
Author(s)
Lidman, T
Sivek, S
Type
Journal Article
Abstract
We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus must have slope , leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston–Bennequin numbers of cables.
Date Issued
2015-09-24
Date Acceptance
2015-05-05
Citation
Compositio Mathematica, 2015, 152 (01), pp.152-186
ISSN
0010-437X
Publisher
Foundation Compositio Mathematica
Start Page
152
End Page
186
Journal / Book Title
Compositio Mathematica
Volume
152
Issue
01
Subjects
math.GT
math.SG
57M25, 57R17
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Date Publish Online
2015-09-24