A note on thickness of knots. (English) Zbl 1522.57020
Baldwin, John A. (ed.) et al., Gauge theory and low-dimensional topology. Progress and interaction. Proceedings of the sixth Banff International Research Station, BIRS, workshop on Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4, virtual, 2020. Berkeley, CA: Mathematical Sciences Publishers (MSP). Open Book Ser. 5, 299-308 (2022).
Summary: We introduce a numerical invariant \(\beta(K)\in \mathbb{N}\cup \{0\}\) of a knot \(K\subset S^3\) which measures how nonalternating \(K\) is. We prove an inequality between \(\beta (K)\) and the (knot Floer) thickness \(th(K)\) of a knot \(K\). As an application we show that all Montesinos knots have thickness at most one.
For the entire collection see [Zbl 1515.57005].
For the entire collection see [Zbl 1515.57005].
MSC:
| 57K10 | Knot theory |
References:
| [1] | 10.1007/s40306-014-0083-y · Zbl 1306.57007 · doi:10.1007/s40306-014-0083-y |
| [2] | 10.1016/j.jctb.2007.08.003 · Zbl 1135.05015 · doi:10.1016/j.jctb.2007.08.003 |
| [3] | 10.1090/memo/0339 · Zbl 1415.57001 · doi:10.1090/memo/0339 |
| [4] | 10.1006/aama.1996.0511 · Zbl 0871.57002 · doi:10.1006/aama.1996.0511 |
| [5] | 10.1215/00127094-2017-0004 · Zbl 1377.57009 · doi:10.1215/00127094-2017-0004 |
| [6] | 10.2140/gt.2017.21.2353 · Zbl 1375.57011 · doi:10.2140/gt.2017.21.2353 |
| [7] | 10.2140/agt.2008.8.1141 · Zbl 1154.57030 · doi:10.2140/agt.2008.8.1141 |
| [8] | 10.2140/gt.2003.7.225 · Zbl 1130.57303 · doi:10.2140/gt.2003.7.225 |
| [9] | ; Turaev, Vladimir G., A simple proof of the Murasugi and Kauffman theorems on alternating links, Enseign. Math. (2), 33, 3-4, 203 (1987) · Zbl 0668.57009 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
