DIMENSION OF CHARACTER VARIETIES FOR 3-MANIFOLDS

作者：Falbel E^*; Guilloux A

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145(6): 2727-2737.

DOI：10.1090/proc/13394

Let M be an orientable 3-manifold, compact with boundary and G its fundamental group. Consider a complex reductive algebraic group G. The character variety X(Gamma, G) is the GIT quotient Hom(Gamma, G)//G of the space of morphisms Gamma -> G by the natural action by conjugation of G. In the case G = SL(2, C) this space has been thoroughly studied.
Following work of Thurston (1980), as presented by Culler-Shalen (1983), we give a lower bound for the dimension of irreducible components of X(G, G) in terms of the Euler characteristic chi(M) of M, the number t of torus boundary components of M, the dimension d and the rank r of G. Indeed, under mild assumptions on an irreducible component X-0 of X(G, G), we prove the inequality
dim(X-0) >= t . r -d(chi)(M).

• 出版日期2017-6
• 单位INRIA