Vassiliev and Quantum Invariants of Braids
Dror Bar-Natan (http://www.ma.huji.ac.il/~drorbn)
TL;DR
This paper demonstrates that quantum gl(N)-based invariants can distinguish all braids by connecting them to Vassiliev invariants, thus confirming their completeness in braid classification.
Contribution
It establishes that all Vassiliev invariants of braids are derived from quantum gl(N) invariants, providing a new proof that these invariants separate braids.
Findings
Quantum gl(N) invariants are all Vassiliev invariants.
Vassiliev invariants of braids are fully captured by quantum invariants.
Quantum invariants distinguish all braids.
Abstract
We prove that braid invariants coming from quantum gl(N) separate braids, by recalling that these invariants (properly decomposed) are all Vassiliev invariants, showing that all Vassiliev invariants of braids arise in this way, and reproving that Vassiliev invariants separate braids. We discuss some corollaries of this result and of our method of proof.
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 · Algebraic structures and combinatorial models · Advanced Operator Algebra Research