Volume 4, issue 1 (2000)

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Splittings of groups and intersection numbers

Peter Scott and Gadde A Swarup

Geometry & Topology 4 (2000) 179–218

arXiv: math.GT/9906004

Abstract

We prove algebraic analogues of the facts that a curve on a surface with self-intersection number zero is homotopic to a cover of a simple curve, and that two simple curves on a surface with intersection number zero can be isotoped to be disjoint.

Keywords
amalgamated free product, splitting, intersection number, ends
Mathematical Subject Classification 2000
Primary: 20E06, 20E08
Secondary: 20F32, 57M07
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Publication
Received: 18 May 1999
Revised: 6 April 2000
Accepted: 24 July 2000
Published: 9 August 2000
Proposed: Jean-Pierre Otal
Seconded: Walter Neumann, Joan Birman
Authors
Peter Scott
Mathematics Department
University of Michigan
Ann Arbor
Michigan 48109
USA
Gadde A Swarup
Mathematics Department
University of Melbourne
Parkville
Victoria 3052
Australia