Journal article
Exceptional and cosmetic surgeries on knots
Mathematische annalen, Vol.367(1-2), pp.581-622
02/01/2017
DOI: 10.1007/s00208-016-1392-3
Abstract
We show that the bridge distance of a knot determines a lower bound on the genera of essential surfaces and Heegaard surfaces in the manifolds that result from non-trivial Dehn surgeries on the knot. In particular, knots with high bridge distance do not admit non-trivial non-hyperbolic surgeries or non-trivial cosmetic surgeries. We further show that if a knot has bridge distance at least 3 then its bridge number is bounded above by a function of Seifert genus, or indeed by the genus of (almost) any essential surface or Heegaard surface in the surgered manifold.
Details
- Title: Subtitle
- Exceptional and cosmetic surgeries on knots
- Creators
- Ryan Blair - California State University, Long BeachMarion Campisi - San Jose State UniversityJesse Johnson - Oklahoma State UniversityScott A Taylor - Colby CollegeMaggy Tomova - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Mathematische annalen, Vol.367(1-2), pp.581-622
- Publisher
- SPRINGER HEIDELBERG
- DOI
- 10.1007/s00208-016-1392-3
- ISSN
- 0025-5831
- eISSN
- 1432-1807
- Number of pages
- 42
- Grant note
- DMS-1006369; DMS-1054450 / NSF American Institute of Mathematics
- Language
- English
- Date published
- 02/01/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984240778902771
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