Limits of (certain) CAT(0) groups, II: The Hopf property and the shortening argument

Abstract

This is the second in a series of papers about torsion-free groups which act properly and cocompactly on a CAT(0) metric space with isolated flats and relatively thin triangles. Our approach is to adapt the methods of Sela and others for word-hyperbolic groups to this context of non-positive curvature. The main result in this paper is that (under certain technical hypotheses) such a group as above is Hopfian. This (mostly) answers a question of Sela.

arXiv comment38 pages

References in corpus (2)

• Accidental parabolics and relatively hyperbolic groups
• Tree-graded spaces and asymptotic cones of groups

Cited by in corpus (6)

• Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams
• Hadamard spaces with isolated flats
• Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness
• Median structures on asymptotic cones and homomorphisms into mapping class groups
• Groups acting on tree-graded spaces and splittings of relatively hyperbolic group
• Lectures notes in universal algebraic geometry