Surface subgroups and handlebody attachment

Easson, Vivien R¹

¹ Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK

Geometry & topology, Tome 10 (2006) no. 1, pp. 557-591.

Résumé

The main theorem of this paper generalizes recent results in Dehn surgery to the case of handlebody attachment. We consider attaching handlebodies and solid tori to the boundary of an irreducible, boundary-irreducible, atoroidal and acylindrical 3–manifold. We show that for a large class of homeomorphisms attaching these handlebodies, the fundamental group of the resulting manifold contains the fundamental group of a closed surface of genus at least two.

Détail

DOI : 10.2140/gt.2006.10.557

Keywords: 3-manifold, handlebody attachment, surface subgroup

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