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2016 The simple loop conjecture for $3$–manifolds modeled on Sol
Drew Zemke
Algebr. Geom. Topol. 16(5): 3051-3071 (2016). DOI: 10.2140/agt.2016.16.3051

Abstract

The simple loop conjecture for 3–manifolds states that every 2–sided immersion of a closed surface into a 3–manifold is either injective on fundamental groups or admits a compression. This can be viewed as a generalization of the loop theorem to immersed surfaces. We prove the conjecture in the case that the target 3–manifold admits a geometric structure modeled on Sol.

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Drew Zemke. "The simple loop conjecture for $3$–manifolds modeled on Sol." Algebr. Geom. Topol. 16 (5) 3051 - 3071, 2016. https://doi.org/10.2140/agt.2016.16.3051

Information

Received: 30 December 2015; Revised: 14 March 2016; Accepted: 28 March 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1353.57021
MathSciNet: MR3572359
Digital Object Identifier: 10.2140/agt.2016.16.3051

Subjects:
Primary: 57M35
Secondary: 57M50

Rights: Copyright © 2016 Mathematical Sciences Publishers

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