The variety of characters in PSL(2,C)
Michael Heusener, Joan Porti
TL;DR
This paper investigates the structure of the character variety in PSL(2,C) for finitely generated groups, providing new examples of 3-manifolds with complex character varieties and analyzing singularities.
Contribution
It introduces a new interpretation of points as characters of representations and constructs 3-manifolds with complex, non-liftable character variety components.
Findings
Constructed 3-manifolds with arbitrarily many non-liftable components
Provided interpretation of points as characters of representations
Analyzed the singular locus of free group character varieties
Abstract
We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of characters has arbitrarily many components that do not lift to SL(2,C). We also study the singular locus of the variety of characters of a free group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · semigroups and automata theory