A colored 𝔰𝔩(N) homology for links in S³

Hao Wu

  • 2014

Abstract

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Fix an integer N ≥ 2. To each diagram of a link colored by 1,...,N we associate a chain complex of graded matrix factorizations. We prove that the homotopy type of this chain complex is invariant under Reidemeister moves. When every component of the link is colored by 1, this chain complex is isomorphic to the chain complex defined by Khovanov and Rozansky. The homology of this chain complex decategorifies to the Reshetikhin-Turaev 𝔰𝔩(N) polynomial of links colored by exterior powers of the defining representation.

How to cite

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Hao Wu. A colored 𝔰𝔩(N) homology for links in S³. 2014. <http://eudml.org/doc/285965>.

@book{HaoWu2014,
abstract = {Fix an integer N ≥ 2. To each diagram of a link colored by 1,...,N we associate a chain complex of graded matrix factorizations. We prove that the homotopy type of this chain complex is invariant under Reidemeister moves. When every component of the link is colored by 1, this chain complex is isomorphic to the chain complex defined by Khovanov and Rozansky. The homology of this chain complex decategorifies to the Reshetikhin-Turaev 𝔰𝔩(N) polynomial of links colored by exterior powers of the defining representation.},
author = {Hao Wu},
keywords = {Reshetikhin-Turaev link invariant; Khovanov-Rozansky homology; matrix factorization; symmetric polynomial},
language = {eng},
title = {A colored 𝔰𝔩(N) homology for links in S³},
url = {http://eudml.org/doc/285965},
year = {2014},
}

TY - BOOK
AU - Hao Wu
TI - A colored 𝔰𝔩(N) homology for links in S³
PY - 2014
AB - Fix an integer N ≥ 2. To each diagram of a link colored by 1,...,N we associate a chain complex of graded matrix factorizations. We prove that the homotopy type of this chain complex is invariant under Reidemeister moves. When every component of the link is colored by 1, this chain complex is isomorphic to the chain complex defined by Khovanov and Rozansky. The homology of this chain complex decategorifies to the Reshetikhin-Turaev 𝔰𝔩(N) polynomial of links colored by exterior powers of the defining representation.
LA - eng
KW - Reshetikhin-Turaev link invariant; Khovanov-Rozansky homology; matrix factorization; symmetric polynomial
UR - http://eudml.org/doc/285965
ER -

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