Abstract
We extend Milnor's μ-invariants of link homotopy to ordered (classical or virtual) tangles. Simple combinatorial formulas for μ-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.
Original language | English |
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Pages (from-to) | 297-316 |
Number of pages | 20 |
Journal | Letters in Mathematical Physics |
Volume | 95 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2011 |
Keywords
- dialgebras
- operads
- planar trees
- tangles
- μ-invariants
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics