Surface subgroups and handlebody attachment

Easson, Vivien R

doi:10.2140/gt.2006.10.557

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Surface subgroups and handlebody attachment

Vivien R Easson

Geometry & Topology 10 (2006) 557–591

DOI: 10.2140/gt.2006.10.557

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

Volume 10, issue 1 (2006)