Representations of 3-manifold groups in PGL(n,C) and their restriction to the boundary

2013/10/10 by Antonin Guilloux, Guilloux, Antonin
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1310.2907

24 pages, 5 figures

arxiv created 2013/10/10 · arxiv updated 2013/10/11

Abstract

We study here the space of representations of a fundamental group of a 3-manifold into PGL(n,C). Thurston, Neumann and Zagier initiated a strategy (in the case of PGL(2,C)) consisting in: triangulate the manifold, assign shapes to each pieces and then try to glue back. This leads to the "gluing equations" and the Neumann-Zagier symplectic space. Building on the works of Dimofte-Gabella-Goncharov and Bergeron-Falbel-Guilloux, we complete the picture in the case of PGL(n,C). We recover a situation very similar to the case of PGL(2,C). This allows for example to obtain a combinatorial proof of a local rigidity results for such representations.

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