English

Local rigidity for PGL(3,C)-representations of 3-manifold groups

Geometric Topology 2013-08-01 v1

Abstract

Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by the gluing equations for PGL(3,C)-representations. In particular we prove local rigidity of the "geometric" representation in PGL(3,C), recovering a recent result of Menal-Ferrer and Porti. More generally we give a criterion for local rigidty of PGL(3,C)-representations and provide detailed analysis of the figure eight knot sister manifold exhibiting the different possibilities that can occur.

Keywords

Cite

@article{arxiv.1307.8343,
  title  = {Local rigidity for PGL(3,C)-representations of 3-manifold groups},
  author = {N. Bergeron and E. Falbel and A. Guilloux and P. -V. Koseleff and F. Rouillier},
  journal= {arXiv preprint arXiv:1307.8343},
  year   = {2013}
}

Comments

15 pages, 4 figures