$U_q(sl(2))$-quantum invariants from an intersection of two Lagrangians in a symmetric power of a surface
| Autor: | Anghel, Cristina Ana-Maria |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we show that coloured Jones and coloured Alexander polynomials can both be read off from the same picture provided by two Lagrangians in a symmetric power of a surface. More specifically, the $N^{th}$ coloured Jones and $N^{th}$ coloured Alexander polynomials are specialisations of a graded intersection between two explicit Lagrangian submanifolds in a symmetric power of the punctured disc. The graded intersection is parametrised by the intersection points between these Lagrangians, graded in a specific manner using the diagonals of the symmetric power. As a particular case, we see the original Jones and Alexander polynomials as two specialisations of a graded intersection between two Lagrangians in a configuration space, whose geometric supports are Heegaard diagrams. Comment: 26 pages |
| Databáze: | arXiv |
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