Geometry & Topology
- Geom. Topol.
- Volume 10, Number 1 (2006), 557-591.
Surface subgroups and handlebody attachment
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.
Geom. Topol., Volume 10, Number 1 (2006), 557-591.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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