Séminaires : Séminaire d'Algèbre

Let M be a compact oriented 3-manifold with boundary consisting of tori. The SL_2 adjoint torsion is a function on the moduli space of SL_2-local systems on M satisfying a regularity condition, which is defined by Porti. In this talk, I will propose an extension of Porti's definition to a general semisimple algebraic group G. According to Zickert’s work, local systems on a 3-manifold with a truncated ideal triangulation can be found by solving the Ptolemy relations, which are relations among cluster variables. Using this method, I will also give an explicit computation of the torsion for the figure-eight knot complement with G = PGSp_4. This is joint work with Tsukasa Ishibashi.

This talk will take place in hybrid mode at the Institut Henri Poincaré.