Splittings of groups and intersection numbers

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

References

Forward citations

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

Volume 4, issue 1 (2000)

Peter Scott and Gadde A Swarup