Splittings of groups and intersection numbers

Peter Scott, G. A. Swarup

Type: Article

Publication Date: 2000-08-09

Citations: 39

DOI: https://doi.org/10.2140/gt.2000.4.179

Abstract

We prove algebraic analogues of the facts that a curve on a surface with selfintersection 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.

Locations

arXiv (Cornell University) - View - PDF
Project Euclid (Cornell University) - View - PDF
DataCite API - View
Geometry & Topology - View - PDF

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Works That Cite This (38)

Action	Title	Year	Authors
+	Canonical decompositions for Poincar\'e duality pairs	2007	Peter Scott G. A. Swarup
+	Comparing decompositions of Poincaré duality pairs	2020	Lawrence Reeves Peter Scott G. A. Swarup
+ PDF Chat	Automorphisms of graphs of cyclic splittings of free groups	2015	Camille Horbez Richard D. Wade
+ PDF Chat	Growth of intersection numbers for free group automorphisms	2010	Jason Behrstock Mladen Bestvina Matt Clay
+	Regular neighbourhoods and canonical decompositions for groups	2018	Peter Scott G. A. Swarup
+	Canonical splittings of groups and 3-manifolds	2001	Peter Scott G. A. Swarup
+ PDF Chat	The geometry of abstract groups and their splittings	2003	C. T. C. Wall
+	The singularity obstruction for group splittings	2002	Graham A. Niblo
+ PDF Chat	Centralisateurs dans les groupes à dualité de Poincaré de dimension 3	2004	Fabrice Castel
+	Algebraic and geometric intersection numbers for free groups	2009	Siddhartha Gadgil Suhas Pandit

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+ PDF Chat	Canonical splittings of groups and 3-manifolds	2001	Peter Scott G. A. Swarup
+	The algebraic torus theorem	2000	M. J. Dunwoody Eric Swenson
+	Splitting Groups Over Polycyclic-By-Finite Subgroups	1993	M. J. Dunwoody Martin A. Roller
+ PDF Chat	An algebraic annulus theorem	2000	G. P. Scott G. A. Swarup
+	Structure and Rigidity in (Gromov) Hyperbolic Groups and Discrete Groups in Rank 1 Lie Groups II	1997	Zlil Sela
+ PDF Chat	Least area incompressible surfaces in 3-manifolds	1983	Michael Freedman Joel Hass Peter Scott
+	Closed Geodesics on Surfaces	1982	Michael Freedman Joel Hass Peter Scott
+	A New Proof of the Annulus and Torus Theorems	1980	Peter Scott
+	Codimension-1 Subgroups and Splittings of Groups	1997	Michah Sageev
+	Accessibility and Groups of Cohomological Dimension One	1979	M. J. Dunwoody