SLn-CHARACTER VARIETIES AS SPACES OF GRAPHS
نویسنده
چکیده
An SLn-character of a groupG is the trace of an SLn-representation of G.We show that all algebraic relations between SLn-characters of G can be visualized as relations between graphs (resembling Feynman diagrams) in any topological space X, with π1(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 SLn-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 SL2-character variety of π1(M). This paper provides a generalization of this result to all SLn-character varieties.
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