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2017 $3$–manifolds built from injective handlebodies
James Coffey, Hyam Rubinstein
Algebr. Geom. Topol. 17(6): 3213-3257 (2017). DOI: 10.2140/agt.2017.17.3213

Abstract

This paper studies a class of closed orientable 3–manifolds constructed from a gluing of three handlebodies, such that the inclusion of each handlebody is π1–injective. This construction is the generalisation to handlebodies of the construction for gluing three solid tori to produce non-Haken Seifert fibred 3–manifolds with infinite fundamental group. It is shown that there is an efficient algorithm to decide if a gluing of handlebodies satisfies the disk-condition. Also, an outline for the construction of the characteristic variety (JSJ decomposition) in such manifolds is given. Some non-Haken and atoroidal examples are given.

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James Coffey. Hyam Rubinstein. "$3$–manifolds built from injective handlebodies." Algebr. Geom. Topol. 17 (6) 3213 - 3257, 2017. https://doi.org/10.2140/agt.2017.17.3213

Information

Received: 21 February 2006; Revised: 19 January 2017; Accepted: 1 March 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1380.57023
MathSciNet: MR3709646
Digital Object Identifier: 10.2140/agt.2017.17.3213

Subjects:
Primary: 57M10, 57M50, 57N10

Rights: Copyright © 2017 Mathematical Sciences Publishers

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