Psybrackets, Pseudoknots and Singular Knots
Suhyeon Jeong, Jieon Kim, Sam Nelson
TL;DR
This paper introduces algebraic structures called psybrackets to define invariants for pseudoknots and singular knots, expanding the toolkit for knot theory with new algebraic methods and examples.
Contribution
The paper develops psybrackets, a new algebraic structure inspired by Reidemeister moves, to create invariants for pseudoknots and singular knots, with explicit examples and computations.
Findings
Psybrackets are a new algebraic structure extending Niebrzydowski tribrackets.
Psybrackets can be used to define invariants of pseudoknots and singular knots.
Examples demonstrate the effectiveness of psybrackets in knot invariants.
Abstract
We introduce algebraic structures known as psybrackets and use them to define invariants of pseudoknots and singular knots and links. Psybrackets are Niebrzydowski tribrackets with additional structure inspired by the Reidemeister moves for pseudoknots and singular knots. Examples and computations are provided.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Logic, programming, and type systems