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THE CONORMAL TORUS IS A COMPLETE KNOT INVARIANT

Part of: Low-dimensional topology Homology and cohomology theories

Published online by Cambridge University Press:  06 September 2019

VIVEK SHENDE Open the ORCID record for VIVEK SHENDE [Opens in a new window]
VIVEK SHENDE*
Affiliation:
Departments of Mathematics, U.C. Berkeley, Berkeley CA 94720, USA; vivek@math.berkeley.edu

Abstract

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We use microlocal sheaf theory to show that knots can only have Legendrian isotopic conormal tori if they themselves are isotopic or mirror images.

MSC classification

Primary: 57M25: Knots and links in $S^3$ 57M27: Invariants of knots and 3-manifolds 55N30: Sheaf cohomology
Type
Research Article
Information
Forum of Mathematics, Pi , Volume 7 , 2019 , e6
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (http://creativecommons.org/licenses/by-nc-sa/4.0/), which permits noncommercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use.
Copyright
© The Author 2019

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