Diassociative Algebras and Milnor's Invariants for Tangles

Olga Kravchenko; Michael Polyak

doi:10.1007/s11005-010-0459-4

Diassociative Algebras and Milnor's Invariants for Tangles

Olga Kravchenko
, Michael Polyak

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	297-316
Number of pages	20
Journal	Letters in Mathematical Physics
Volume	95
Issue number	3
DOIs	https://doi.org/10.1007/s11005-010-0459-4
State	Published - Mar 2011

Keywords

dialgebras
operads
planar trees
tangles
μ-invariants

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-010-0459-4

Cite this

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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.",

keywords = "dialgebras, operads, planar trees, tangles, μ-invariants",

author = "Olga Kravchenko and Michael Polyak",

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year = "2011",

month = mar,

doi = "10.1007/s11005-010-0459-4",

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volume = "95",

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T1 - Diassociative Algebras and Milnor's Invariants for Tangles

AU - Kravchenko, Olga

AU - Polyak, Michael

N1 - Funding Information: The second author was partially supported by the ISF grant 1343/10.

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

KW - dialgebras

KW - operads

KW - planar trees

KW - tangles

KW - μ-invariants

UR - https://www.scopus.com/pages/publications/79952194386

U2 - 10.1007/s11005-010-0459-4

DO - 10.1007/s11005-010-0459-4

M3 - مقالة

SN - 0377-9017

VL - 95

SP - 297

EP - 316

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 3

ER -

Diassociative Algebras and Milnor's Invariants for Tangles

Abstract

Keywords

ASJC Scopus subject areas

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