Geodesic
3–manifolds built from injective handlebodies
Coffey, James1 ; Rubinstein, Hyam2
1 Northcote, Victoria, Australia
2 Department of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria, Australia
Algebraic and Geometric Topology, Tome 17 (2017) no. 6, pp. 3213-3257

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2017.17.3213
Classification : 57N10, 57M10, 57M50
Keywords: 3–manifolds, handlebodies, infinite fundamental group, non-Haken

Coffey, James 1 ; Rubinstein, Hyam 2

1 Northcote, Victoria, Australia
2 Department of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria, Australia 
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Coffey, James; Rubinstein, Hyam. 3–manifolds built from injective handlebodies. Algebraic and Geometric Topology, Tome 17 (2017) no. 6, pp. 3213-3257. doi: 10.2140/agt.2017.17.3213

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