Geometry & Topology

Surface subgroups and handlebody attachment

Vivien R Easson

Full-text: Open access

Abstract

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.

Article information

Source
Geom. Topol., Volume 10, Number 1 (2006), 557-591.

Dates
Received: 4 March 2004
Revised: 19 July 2005
Accepted: 25 March 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799715

Digital Object Identifier
doi:10.2140/gt.2006.10.557

Mathematical Reviews number (MathSciNet)
MR2224465

Zentralblatt MATH identifier
1128.57019

Subjects
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M50: Geometric structures on low-dimensional manifolds 57N35: Embeddings and immersions 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]

Keywords
3-manifold handlebody attachment surface subgroup

Citation

Easson, Vivien R. Surface subgroups and handlebody attachment. Geom. Topol. 10 (2006), no. 1, 557--591. doi:10.2140/gt.2006.10.557. https://projecteuclid.org/euclid.gt/1513799715


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