-character varieties as spaces of graphs

Author:
Adam S. Sikora

Journal:
Trans. Amer. Math. Soc. **353** (2001), 2773-2804

MSC (1991):
Primary 20C15, 57M27

DOI:
https://doi.org/10.1090/S0002-9947-01-02700-3

Published electronically:
March 15, 2001

MathSciNet review:
1828473

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

An -character of a group is the trace of an -representation of We show that all algebraic relations between -characters of can be visualized as relations between graphs (resembling Feynman diagrams) in any topological space with 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 -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 which, by a theorem of Bullock, Przytycki, and the author, is a deformation of the -character variety of This paper provides a generalization of this result to all -character varieties.

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Additional Information

**Adam S. Sikora**

Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742

Email:
asikora@math.umd.edu

DOI:
https://doi.org/10.1090/S0002-9947-01-02700-3

Keywords:
Character,
character variety,
skein module

Received by editor(s):
May 18, 1999

Received by editor(s) in revised form:
August 9, 2000

Published electronically:
March 15, 2001

Additional Notes:
Partially supported by NSF grant DMS93-22675

Article copyright:
© Copyright 2001
American Mathematical Society