Volume 17, issue 6 (2017)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
$3$–manifolds built from injective handlebodies

James Coffey and Hyam Rubinstein

Algebraic & Geometric Topology 17 (2017) 3213–3257
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 ${\pi }_{1}$–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.

Keywords
3–manifolds, handlebodies, infinite fundamental group, non-Haken
Mathematical Subject Classification 2010
Primary: 57N10, 57M10, 57M50
Publication
Received: 21 February 2006
Revised: 19 January 2017
Accepted: 1 March 2017
Published: 4 October 2017
Authors
 James Coffey Northcote Victoria Australia Hyam Rubinstein Department of Mathematics and Statistics The University of Melbourne Parkville Victoria Australia http://www.ms.unimelb.edu.au/~rubin/