Diassociative Algebras and Milnor's Invariants for Tangles

Olga Kravchenko, Michael Polyak

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)297-316
Number of pages20
JournalLetters in Mathematical Physics
Volume95
Issue number3
DOIs
StatePublished - Mar 2011

Keywords

  • dialgebras
  • operads
  • planar trees
  • tangles
  • μ-invariants

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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