Diassociative algebras and Milnor's invariants for tangles
Olga Kravchenko, Michael Polyak
TL;DR
This paper extends Milnor's invariants to ordered tangles, providing combinatorial formulas via Gauss diagrams and linking invariance to diassociative algebra axioms.
Contribution
It introduces a new framework connecting Milnor's invariants for tangles with diassociative algebra structures through combinatorial formulas and operad morphisms.
Findings
Milnor's mu-invariants extended to tangles
Combinatorial formulas using Gauss diagrams
Invariance linked to diassociative algebra axioms
Abstract
We extend Milnor's mu-invariants of link homotopy to ordered (classical or virtual) tangles. Simple combinatorial formulas for mu-invariants are given in terms of counting trees in Gauss diagrams. Invariance under Reidemeister moves corresponds to axioms of Loday's diassociative algebra. The relation of tangles to diassociative algebras is formulated in terms of a morphism of corresponding operads.
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.