Journal article
Kirby-Thompson distance for trisections of knotted surfaces
Journal of the London Mathematical Society, Vol.105(2), pp.765-793
03/01/2022
DOI: 10.1112/jlms.12513
Abstract
We adapt work of Kirby-Thompson and Zupan to define an integer invariant L(T)$\mathcal {L}(\mathcal {T})$ of a bridge trisection T$\mathcal {T}$ of a smooth surface S$S$ in S4$S<^>4$ or B4$B<^>4$. We show that when L(T)=0$\mathcal {L}(\mathcal {T})=0$, then the surface S$S$ is unknotted. We also show that for a trisection T$\mathcal {T}$ of an irreducible surface, bridge number produces a lower bound for L(T)$\mathcal {L}(\mathcal {T})$. Consequently L$\mathcal {L}$ can be arbitrarily large.
Details
- Title: Subtitle
- Kirby-Thompson distance for trisections of knotted surfaces
- Creators
- Ryan Blair - Calif State Univ Long Beach, Dept Math, Long Beach, CA 90840 USAMarion Campisi - San Jose State UniversityScott A Taylor - Colby Coll, Dept Math, 5832 Mayflower Hill, Waterville, ME 04901 USAMaggy Tomova - Univ Iowa, Dept Math, Coll Liberal Arts & Sci, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Journal of the London Mathematical Society, Vol.105(2), pp.765-793
- DOI
- 10.1112/jlms.12513
- ISSN
- 0024-6107
- eISSN
- 1469-7750
- Publisher
- WILEY
- Number of pages
- 29
- Grant note
- Colby College Research Grant DMS-1821254 / NSF; National Science Foundation (NSF) San Jose State University RSCA Grant
- Language
- English
- Date published
- 03/01/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984240779602771
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