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Essential loops in taut ideal triangulations

Saul Schleimer and Henry Segerman
Algebraic & Geometric Topology 20 (2020) 487–501
DOI: 10.2140/agt.2020.20.487
Abstract

In this note we combinatorialise a technique of Novikov. We use this to prove that, in a three-manifold equipped with a taut ideal triangulation, any vertical or normal loop is nontrivial in the fundamental group.

Keywords
taut, ideal triangulations, essential loops
Mathematical Subject Classification 2010
Primary: 57M05
Secondary: 57M20
References
Publication
Received: 10 March 2019
Revised: 31 May 2019
Accepted: 17 June 2019
Published: 23 February 2020
Authors
Saul Schleimer
Mathematics Institute
University of Warwick
Coventry
United Kingdom
http://homepages.warwick.ac.uk/~masgar/
Henry Segerman
Department of Mathematics
Oklahoma State University
Stillwater, OK
United States
https://math.okstate.edu/people/segerman/