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Geography of Legendrian knot mosaics.
- Source :
-
Journal of Knot Theory & Its Ramifications . Jan2022, Vol. 31 Issue 1, p1-22. 22p. - Publication Year :
- 2022
-
Abstract
- In this paper, mosaic tiles have been used to build knots and define invariants since they were introduced by Lomonaco and Kauffman to describe quantum knots. In this paper, we propose a modified set of tiles to describe the front projections of Legendrian knots. We explore the effect of stabilization on the mosaic number of a Legendrian knot by defining and classifying "two-cell" stabilizations. Inspired by a construction of Ludwig et al. in 2013, we provide an infinite family of Legendrian unknots whose mosaic numbers are realized only in non-reduced projections. Finally, we provide a census of known mosaic numbers for Legendrian unknots and trefoils. [ABSTRACT FROM AUTHOR]
- Subjects :
- *TILES
*CENSUS
*GEOGRAPHY
Subjects
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 31
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 156509134
- Full Text :
- https://doi.org/10.1142/S021821652250002X