Algorithmic unsolvability of the triviality problem for multidimensional knots.
All CAT(0) boundaries of a group of the form H × K are CE equivalent
M. Bestvina has shown that for any given torsion-free CAT(0) group G, all of its boundaries are shape equivalent. He then posed the question of whether they satisfy the stronger condition of being cell-like equivalent. In this article we prove that the answer is "Yes" in the situation where the group in question splits as a direct product with infinite factors. We accomplish this by proving an interesting theorem in shape theory.
All compact manifolds are homeomorphic to totally algebraic real algebraic sets.
All flat manifolds are cusps of hyperbolic orbifolds.
All integral slopes can be Seifert fibered slopes for hyperbolic knots.
All Knot Groups Are Metric.
All knots are algebraic.
All natural concomitants of vector valued differential forms
All roots of unity are detected by the A-polynomial.
All two dimensions links are null homotopic.
Allgemeine Lage und äquivariante Homotopie.
Almost Canonical Inverse Images
Almost complex toric manifolds and positive line bundles
Almost integral TQFTs from simple Lie algebras.
Almost invariant submanifolds for compact group actions
We define a distance between submanifolds of a riemannian manifold and show that, if a compact submanifold is not moved too much under the isometric action of a compact group , there is a -invariant submanifold -close to . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros of sections...
Almost transitive actions on spaces with the rational homotopy of sphere products.
Almost-Bieberbach groups with prime order holonomy
The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds. That is: we look for infra-nilmanifolds with prime order holonomy which can be obtained as a fiber space with a non-trivial nilmanifold as fiber and an infra-nilmanifold as its base. In this perspective, we prove the following algebraic result: if E is an almost-Bieberbach group with prime order holonomy,...
Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property
We show that the amalgamated free products of two free groups over a cyclic subgroup admit amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on two generators.
Amenable groups and Euler characteristic.
Amenable Groups and Stabilizers of Measures on the Boundary of a Hadamard Manifold.