Volume 13, issue 4 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Closed surfaces and character varieties

Eric Chesebro

Algebraic & Geometric Topology 13 (2013) 2001–2037
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