Volume 10, issue 1 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Surface subgroups and handlebody attachment

Vivien R Easson

Geometry & Topology 10 (2006) 557–591

arXiv: math/0403077

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.

Keywords
3-manifold, handlebody attachment, surface subgroup
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M50, 57N35, 20H10
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Publication
Received: 4 March 2004
Revised: 19 July 2005
Accepted: 25 March 2006
Published: 4 May 2006
Proposed: Cameron Gordon
Seconded: Joan Birman, Colin Rourke
Authors
Vivien R Easson
Centre for Mathematical Sciences
University of Cambridge
Wilberforce Road
Cambridge CB3 0WB, UK
http://www.dpmms.cam.ac.uk/~vre20