Algebraic & Geometric Topology

$3$–manifolds built from injective handlebodies

James Coffey and Hyam Rubinstein

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 57M10: Covering spaces 57M50: Geometric structures on low-dimensional manifolds

3–manifolds handlebodies infinite fundamental group non-Haken


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.

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