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$3$–manifolds built from injective handlebodies

James Coffey and Hyam Rubinstein

Algebraic & Geometric Topology 17 (2017) 3213–3257

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.

3–manifolds, handlebodies, infinite fundamental group, non-Haken
Mathematical Subject Classification 2010
Primary: 57N10, 57M10, 57M50
Received: 21 February 2006
Revised: 19 January 2017
Accepted: 1 March 2017
Published: 4 October 2017
James Coffey
Hyam Rubinstein
Department of Mathematics and Statistics
The University of Melbourne