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- W3006716436 abstract "Coloured Jones and Alexander polynomials are sequences of quantum invariants recovering the Jones and Alexander polynomials at the first terms. We show that they can be seen conceptually in the same manner, using topological tools, as intersection pairings in covering spaces between explicit homology classes given by Lagrangian submanifolds. The main result proves that the $N^{th}$ coloured Jones polynomial and $N^{th}$ coloured Alexander polynomial come as different specialisations of an intersection pairing of the same homology classes over two variables, with extra framing corrections in each case. The first corollary explains Bigelow's picture for the Jones polynomial with noodles and forks from the quantum point of view. Secondly, we conclude that the $N^{th}$ coloured Alexander polynomial is a graded intersection pairing in a $ mathbb Z oplus mathbb Z_N$-covering of the configuration space in the punctured disc." @default.
- W3006716436 created "2020-03-06" @default.
- W3006716436 creator A5039415321 @default.
- W3006716436 date "2020-02-21" @default.
- W3006716436 modified "2023-09-27" @default.
- W3006716436 title "Coloured Jones and Alexander polynomials as topological intersections of cycles in configuration spaces" @default.
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