Sl_n-character varieties as spaces of graphs

Details Sl_n-character varieties as spaces of graphs Sl_n-character varieties as spaces of graphs

1998-06-03

arxiv.org/abs/math/9806016v2

Mathematics

Representation Theory

This is a new version of my earlier paper "A geometric method in the theory of SL_n-representations of groups" which mentions

Scientific paper

An SL_n-character of a group G is the trace of an SL_n-representation of G. We show that all algebraic relations between SL_n-characters of G can be visualized as relations between graphs (resembling Feynman diagrams) in any topological space X, with pi_1(X)=G. We also show that all such relations are implied by a single local relation between graphs. In this way, we provide a topological approach to the study of SL_n-representations of groups. The motivation for this paper was our work with J. Przytycki on invariants of links in 3-manifolds which are based on the Kauffman bracket skein relation. These invariants lead to a notion of a skein module of M which, by a theorem of Bullock, Przytycki, and the author, is a deformation of the SL_2-character variety of pi_1(M). This paper provides a generalization of this result to all SL_n-character varieties.

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