Closed surfaces and character varieties

Chesebro, Eric

doi:10.2140/agt.2013.13.2001

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Closed surfaces and character varieties

Eric Chesebro

Algebraic & Geometric Topology 13 (2013) 2001–2037

DOI: 10.2140/agt.2013.13.2001

Abstract

The powerful character variety techniques of Culler and Shalen can be used to find essential surfaces in knot manifolds. We show that module structures on the coordinate ring of the character variety can be used to identify detected boundary slopes as well as when closed surfaces are detected. This approach also yields new number theoretic invariants for the character varieties of knot manifolds.

Keywords

3–manifold, character variety, essential surface

Mathematical Subject Classification 2010

Primary: 57M27

References

Publication

Received: 22 February 2013

Accepted: 3 March 2013

Published: 29 May 2013

Authors

Eric Chesebro
Department of Mathematical Sciences University of Montana Mathematics Building (MMAI01) Missoula, MT 59812-0864 USA

Volume 13, issue 4 (2013)