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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

Splittings of groups and intersection numbers

Peter Scott and Gadde A Swarup

Geometry & Topology 4 (2000) 179–218

DOI: 10.2140/gt.2000.4.179

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

Primary: 20E06, 20E08

Secondary: 20F32, 57M07

References
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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