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A
Khovanov stable homotopy type for colored links
Andrew Lobb, Patrick Orson and Dirk Schütz |
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Algebraic & Geometric Topology 17 (2017) 1261–1281
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Abstract |
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We extend Lipshitz and Sarkar’s definition of a stable homotopy type associated to a link whose cohomology recovers the Khovanov cohomology of . Given an assignment (called a coloring) of a positive integer to each component of a link , we define a stable homotopy type whose cohomology recovers the –colored Khovanov cohomology of . This goes via Rozansky’s definition of a categorified Jones–Wenzl projector as an infinite torus braid on strands. We then observe that Cooper and Krushkal’s explicit definition of also gives rise to stable homotopy types of colored links (using the restricted palette ), and we show that these coincide with . We use this equivalence to compute the stable homotopy type of the –colored Hopf link and the –colored trefoil. Finally, we discuss the Cooper–Krushkal projector and make a conjecture of for the unknot. |
Keywords
Khovanov, flow category, stable homotopy type
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Mathematical Subject Classification 2010
Primary: 57M27
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References |
Publication
Received: 27 April 2016
Revised: 12 August 2016
Accepted: 21 August 2016
Published: 14 March 2017
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Authors |
| Andrew Lobb | |
| Department of Mathematical
Sciences Durham University Lower Mountjoy Stockton Road Durham DH1 3LE United Kingdom |
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| Patrick Orson | |
| Département de Mathématiques Université du Québec à Montréal Montréal, Québec H3C 3P8 Canada |
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| Dirk Schütz | |
| Department of Mathematical
Sciences Durham University Lower Mountjoy Stockton Road Durham DH1 3LE United Kingdom |
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