Geometry & Topology, Vol. 4 (2000) Paper no. 6, pages 179--218.

Splittings of groups and intersection numbers

Peter Scott, Gadde A Swarup

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

AMS subject classification. Primary: 20E06, 20E08. Secondary: 20F32, 57M07.

DOI: 10.2140/gt.2000.4.179

E-print: arXiv:math.GT/9906004

Submitted to GT on 18 May 1999. (Revised 6 April 2000.) Paper accepted 24 July 2000. Paper published 9 August 2000.

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Peter Scott, Gadde A Swarup
Mathematics Department, University of Michigan
Ann Arbor, Michigan 48109, USA

Mathematics Department, University of Melbourne
Parkville, Victoria 3052, Australia

Email: pscott@math.lsa.umich.edu, gadde@ms.unimelb.edu.au

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