Geodesic
Colored Khovanov–Rozansky homology for infinite braids
Abel, Michael1 ; Willis, Michael2
1 Department of Mathematics, Duke University, Durham, NC, United States
2 Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 5, pp. 2401-2438

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We show that the limiting unicolored sl(N) Khovanov–Rozansky chain complex of any infinite positive braid categorifies a highest-weight projector. This result extends an earlier result of Cautis categorifying highest-weight projectors using the limiting complex of infinite torus braids. Additionally, we show that the results hold in the case of colored homfly–pt Khovanov–Rozansky homology as well. An application of this result is given in finding a partial isomorphism between the homfly–pt homology of any braid positive link and the stable homfly–pt homology of the infinite torus knot as computed by Hogancamp.

DOI : 10.2140/agt.2019.19.2401
Classification : 57M27
Keywords: Khovanov homology, Khovanov–Rozansky homology, link homology, colored link homology, colored Khovanov–Rozanksy homology, infinite braids, infinite twist

Abel, Michael 1 ; Willis, Michael 2

1 Department of Mathematics, Duke University, Durham, NC, United States
2 Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, United States 
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     title = {Colored {Khovanov{\textendash}Rozansky} homology for infinite braids},
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Abel, Michael; Willis, Michael. Colored Khovanov–Rozansky homology for infinite braids. Algebraic and Geometric Topology, Tome 19 (2019) no. 5, pp. 2401-2438. doi: 10.2140/agt.2019.19.2401

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