3–manifolds built from injective handlebodies

Coffey, James; Rubinstein, Hyam

doi:10.2140/agt.2017.17.3213

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$3$–manifolds built from injective handlebodies

James Coffey and Hyam Rubinstein

Algebraic & Geometric Topology 17 (2017) 3213–3257

DOI: 10.2140/agt.2017.17.3213

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 $π_{1}$ –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

References

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/

Volume 17, issue 6 (2017)