5 papers
Regular Neighbourhoods and Canonical Decompositions for Groups
Peter Scott, Gadde Swarup
We find canonical decompositions for finitely presented groups which specialize to the classical JSJ-decomposition when restricted to the fundamental groups of Haken manifolds. The…
Canonical splittings of groups and 3-manifolds
Peter Scott, Gadde Swarup
We introduce the notion of a `canonical' splitting over Z or ZxZ for a finitely generated group G. We show that when G happens to be the fundamental group of an orientable Haken ma…
Configurations of curves and geodesics on surfaces
Joel Hass, Peter Scott
We study configurations of immersed curves in surfaces and surfaces in 3-manifolds. Among other results, we show that primitive curves have only finitely many configurations which…
Simple Closed Geodesics in Hyperbolic 3-Manifolds
Colin Adams, Joel Hass, Peter Scott
This paper determines which orientable hyperbolic 3-manifolds contain simple closed geodesics. The Fuchsian group corresponding to the thrice-punctured sphere generates the only ex…
A Geometric Characteristic Splitting in all Dimensions
Bernhard Leeb, Peter Scott
We prove the existence of a geometric characteristic submanifold for non-positively curved manifolds of any dimension greater than or equal to three. In dimension three, our result…