Algebraic & Geometric Topology

A signature invariant for knotted Klein graphs

Catherine Gille and Louis-Hadrien Robert

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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.

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 6 (2018), 3719-3747.

Dates
Received: 9 May 2018
Revised: 19 June 2018
Accepted: 30 June 2018
First available in Project Euclid: 27 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.agt/1540605655

Digital Object Identifier
doi:10.2140/agt.2018.18.3719

Mathematical Reviews number (MathSciNet)
MR3868233

Zentralblatt MATH identifier
06990076

Subjects
Primary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 57M12: Special coverings, e.g. branched 57M15: Relations with graph theory [See also 05Cxx]
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

Keywords
knotted trivalent graphs branched covering signature invariants

Citation

Gille, Catherine; Robert, Louis-Hadrien. A signature invariant for knotted Klein graphs. Algebr. Geom. Topol. 18 (2018), no. 6, 3719--3747. doi:10.2140/agt.2018.18.3719. https://projecteuclid.org/euclid.agt/1540605655


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