Contact structures and reducible surgeries

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Title: Contact structures and reducible surgeries
Authors: Lidman, T
Sivek, S
Item 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.
Issue Date: 24-Sep-2015
Date of Acceptance: 5-May-2015
DOI: 10.1112/S0010437X15007599
ISSN: 0010-437X
Publisher: Foundation Compositio Mathematica
Start Page: 152
End Page: 186
Journal / Book Title: Compositio Mathematica
Volume: 152
Issue: 01
Keywords: math.GT
57M25, 57R17
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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