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A signature invariant for knotted Klein graphs

Catherine Gille and Louis-Hadrien Robert

Algebraic & Geometric Topology 18 (2018) 3719–3747
Abstract

We define some signature invariants for a class of knotted trivalent graphs using branched covers. We relate them to classical signatures of knots and links. Finally, we explain how to compute these invariants through the example of Kinoshita’s knotted theta graph.

Keywords
knotted trivalent graphs, branched covering, signature invariants
Mathematical Subject Classification 2010
Primary: 05C10, 57M12, 57M15
Secondary: 57M25, 57M27
References
Publication
Received: 9 May 2018
Revised: 19 June 2018
Accepted: 30 June 2018
Published: 18 October 2018
Authors
Catherine Gille
Institut de Mathématiques de Jussieu-Paris Rive Gauche
CNRS
Sorbonne Université
Université Paris Diderot
Paris
France
https://webusers.imj-prg.fr/catherine.gille
Louis-Hadrien Robert
Section de Mathématiques
Université de Genève
Genève
Switzerland
http://www.unige.ch/math/folks/robert/