Lie algebras of curves and loop-bundles on surfaces
Resumen:
W. Goldman and V. Turaev defined a Lie bialgebra structure on the Z-module generated by free homotopy classes of loops of an oriented surface (i.e. the conjugacy classes of its fundamental group). We develop a generalization of this construction replacing homotopies by thin homotopies, based on the combinatorial approach given by M.Chas. We use it to give a geometric proof of a characterization of simple curves in terms of the Goldman-Turaev bracket, which was conjectured by Chas.
| 2022 | |
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Loop spaces Goldman bracket |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/42367 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
