## Algebraic & Geometric Topology

### $3$–manifolds built from injective handlebodies

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 17, Number 6 (2017), 3213-3257.

Dates
Revised: 19 January 2017
Accepted: 1 March 2017
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841506

Digital Object Identifier
doi:10.2140/agt.2017.17.3213

Mathematical Reviews number (MathSciNet)
MR3709646

Zentralblatt MATH identifier
1380.57023

#### Citation

Coffey, James; Rubinstein, Hyam. $3$–manifolds built from injective handlebodies. Algebr. Geom. Topol. 17 (2017), no. 6, 3213--3257. doi:10.2140/agt.2017.17.3213. https://projecteuclid.org/euclid.agt/1510841506

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