Diassociative algebras and Milnor's invariants for tangles
Geometric Topology
2015-05-20 v2 Quantum Algebra
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.
Cite
@article{arxiv.1011.0117,
title = {Diassociative algebras and Milnor's invariants for tangles},
author = {Olga Kravchenko and Michael Polyak},
journal= {arXiv preprint arXiv:1011.0117},
year = {2015}
}
Comments
17 pages, many figures; v2: several typos corrected