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2012 On Legendrian graphs
Danielle O’Donnol, Elena Pavelescu
Algebr. Geom. Topol. 12(3): 1273-1299 (2012). DOI: 10.2140/agt.2012.12.1273

Abstract

We investigate Legendrian graphs in (3,ξstd). We extend the Thurston–Bennequin number and the rotation number to Legendrian graphs. We prove that a graph can be Legendrian realized with all its cycles Legendrian unknots with tb=1 and rot=0 if and only if it does not contain K4 as a minor. We show that the pair (tb,rot) does not characterize a Legendrian graph up to Legendrian isotopy if the graph contains a cut edge or a cut vertex. When we restrict to planar spatial graphs, a pair (tb,rot) determines two Legendrian isotopy classes of the lollipop graph and a pair (tb,rot) determines four Legendrian isotopy classes of the handcuff graph.

Citation

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Danielle O’Donnol. Elena Pavelescu. "On Legendrian graphs." Algebr. Geom. Topol. 12 (3) 1273 - 1299, 2012. https://doi.org/10.2140/agt.2012.12.1273

Information

Received: 11 October 2011; Revised: 31 January 2012; Accepted: 28 February 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1257.57009
MathSciNet: MR2966686
Digital Object Identifier: 10.2140/agt.2012.12.1273

Subjects:
Primary: 57M25, 57M50
Secondary: 05C10

Rights: Copyright © 2012 Mathematical Sciences Publishers

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