Splittings of groups and intersection numbers

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.

40 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper6.abs.html

References in corpus (2)

• Canonical decompositions of 3-manifolds
• The symmetry of intersection numbers in group theory

Cited by in corpus (4)

• Automorphisms of graphs of cyclic splittings of free groups
• Fully irreducible Automorphisms of the Free Group via Dehn twisting in ${♯}_k(S^2\times S^1)$
• Quasi-Isometry Invariance of Group Splittings over Coarse Poincaré Duality Groups
• Splittings of Non-Finitely Generated Groups