3-manifolds built from injective handlebodies

J. Coffey; H. Rubinstein

doi:10.2140/agt.2017.17.3213

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arXiv · math/0601718

3-manifolds built from injective handlebodies

J. Coffey·H. Rubinstein

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Abstract

This paper looks at 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 condition for gluing three solid tori to produce non-Haken Seifert fibered 3-manifolds with infinite fundamental group. It is shown that there is an efficient algorithm to decide if a gluing of handlebodies meets 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.

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BibTeX RIS

J. Coffey, H. Rubinstein. 2006-01-30. 3-manifolds built from injective handlebodies. https://doi.org/10.2140/agt.2017.17.3213

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