Representation spaces of pretzel knots

Zentner, Raphael

doi:10.2140/agt.2011.11.2941

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Representation spaces of pretzel knots

Raphael Zentner

Algebraic & Geometric Topology 11 (2011) 2941–2970

DOI: 10.2140/agt.2011.11.2941

Abstract

We study the representation spaces $R (K; i)$ appearing in Kronheimer and Mrowka’s instanton knot Floer homologies for a class of pretzel knots. In particular, for pretzel knots $P (p, q, r)$ with $p, q, r$ pairwise coprime, these appear to be nondegenerate and comprise representations in $SU (2)$ that are not binary dihedral.

Keywords

knot, pretzel knot, representation space, $\mathrm{SU}(2)$, instanton knot Floer homology

Mathematical Subject Classification 2000

Primary: 57M25, 57M27

Secondary: 57R58

References

Publication

Received: 16 August 2010

Revised: 8 October 2011

Accepted: 10 October 2011

Published: 12 November 2011

Authors

Raphael Zentner
Mathematisches Institut Universität zu Köln Weyertal 86-90 D-D-50931 Köln Germany

Volume 11, issue 5 (2011)