Legendrian Rack Invariants of Legendrian Knots
Geometric Topology
2021-01-26 v2 Quantum Algebra
Abstract
We define a new algebraic structure called Legendrian racks or racks with Legendrian structure, motivated by the front-projection Reidemeister moves for Legendrian knots. We provide examples of Legendrian racks and use these algebraic structures to define invariants of Legendrian knots with explicit computational examples. We classify Legendrian structures on racks with 3 and 4 elements. We use Legendrian racks to distinguish certain Legendrian knots which are equivalent as smooth knots.
Keywords
Cite
@article{arxiv.1905.06432,
title = {Legendrian Rack Invariants of Legendrian Knots},
author = {Jose Ceniceros and Mohamed Elhamdadi and Sam Nelson},
journal= {arXiv preprint arXiv:1905.06432},
year = {2021}
}
Comments
15 pages. Version 2 includes small corrections suggested by Referee. To appear in Communications of the Korean Mathematical Society