Linearization of the Goldman-Turaev BV algebra using Kashiwara-Vergne theory
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| Title | Linearization of the Goldman-Turaev BV algebra using Kashiwara-Vergne theory |
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| Number of Parts | 15 |
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| License | You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor. |
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| Abstract | Using local intersections, Goldman and Turaev defined a BV operator on the exterior algebra of homotopy classes of loops on a surface. On a genus zero surface with three boundary components the linearization problem of this structure is equivalent to the Kashiwara-Vergne problem in Lie theory. Motivated by this result a generalization of the Kashiwara-Vergne problem in higher genera is proposed and solutions are constructed in analogy with elliptic associators. This is joint work with A. Alekseev, N. Kawazumi and Y. Kuno. |
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