639 research outputs found
Finiteness and the falsification by fellow traveler property
We prove that groups enjoying the falsification by fellow traveler property
are of type , and have at most an exponential second order isoperimetric
function.Comment: Appeared in 2002. I am putting all my past publications on arxi
CAT(0) is an algorithmic property
In this article we give an explicit algorithm which will determine, in a
discrete and computable way, whether a finite piecewise Euclidean complex is
non-positively curved. In particular, given such a complex we show how to
define a boolean combination of polynomial equations and inequalities in real
variables, i.e. a real semi-algebraic set, which is empty if and only if the
complex is non-positively curved. Once this equivalence has been shown, the
main result follows from a standard theorem in real algebraic geometry.Comment: (23 pages) To appear in Geometriae Dedicat
Some geodesic problems in groups
We consider several algorithmic problems concerning geodesics in finitely
generated groups. We show that the three geodesic problems considered by
Miasnikov et al [arXiv:0807.1032] are polynomial-time reducible to each other.
We study two new geodesic problems which arise in a previous paper of the
authors and Fusy [arXiv:0902.0202] .Comment: 6 page
Logspace computations for Garside groups of spindle type
M. Picantin introduced the notion of Garside groups of spindle type,
generalizing the 3-strand braid group. We show that, for linear Garside groups
of spindle type, a normal form and a solution to the conjugacy problem are
logspace computable. For linear Garside groups of spindle type with homogenous
presentation we compute a geodesic normal form in logspace.Comment: 22 pages; short version as v1. Terminolgy and title changed. In
particular, in previous versions we called Garside groups of spindle type
"rigid Garside groups
Combinatorial conditions that imply word-hyperbolicity for 3-manifolds
Thurston conjectured that a closed triangulated 3-manifold in which every
edge has degree 5 or 6, and no two edges of degree 5 lie in a common 2-cell,
has word-hyperbolic fundamental group. We establish Thurston's conjecture by
proving that such a manifold admits a piecewise Euclidean metric of
non-positive curvature and the universal cover contains no isometrically
embedded flat planes. The proof involves a mixture of computer computation and
techniques from small cancellation theory.Comment: (21 pages) To appear in Topolog
A non-Hopfian almost convex group
In this article we prove that an "isometric multiple HNN-extension" of a
group satisfying the falsification by fellow traveler property is almost
convex. As a corollary, Wise's example of a CAT(0) non-Hopfian group is Almost
convex.Comment: Appeared in 2004. I am putting all my past papers on arxi
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