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

Antonin Guilloux

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arXiv · 1310.2907

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

Antonin Guilloux

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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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BibTeX RIS

Antonin Guilloux. 2013-10-10. Representations of 3-manifold groups in PGL(n,C) and their restriction to the boundary. https://arxiv.org/abs/1310.2907

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