Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 17, Number 6 (2017), 3213-3257.
$3$–manifolds built from injective handlebodies
This paper studies a class of closed orientable –manifolds constructed from a gluing of three handlebodies, such that the inclusion of each handlebody is –injective. This construction is the generalisation to handlebodies of the construction for gluing three solid tori to produce non-Haken Seifert fibred –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.
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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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