The goal of this paper is to introduce a new algebraic structure for coloring regions in the planar complement of an oriented virtual knot or link diagram that I will refer to as virtual tribrackets. I will begin with an overview of classical knot theory where I introduce knot diagrams and ways of calculating knot invariants. This paper progresses into virtual knots and links, their geometric interpretations as well as their virtual moves, and some invariant examples for the virtual case. This informations allows me to introduce tribrackets, which is a labeling method used to define counting invariants for classical knots and link diagrams. Finally, this paper properly defines and proves the use of virtual tribackets in defining invariants for virtual knots as well as providing examples from [6] which more precisely show that these invariants can distinguish between certain virtual knots.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:cmc_theses-3000 |
| Date | 01 January 2018 |
| Creators | Pico, Shane |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | CMC Senior Theses |
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