Diassociative algebras and Milnor's invariants for tangles

Details Diassociative algebras and Milnor's invariants for tangles Diassociative algebras and Milnor's invariants for tangles

2010-10-31

arxiv.org/abs/1011.0117v2

Letters Math. Physics 95 (2011), 297--316

Mathematics

Geometric Topology

17 pages, many figures; v2: several typos corrected

Scientific paper

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.

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