Volume 11, issue 5 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Representation spaces of pretzel knots

Raphael Zentner

Algebraic & Geometric Topology 11 (2011) 2941–2970
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