Some results and conjectures on finite groups acting on homology spheres.
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Stable actions of groups on real trees.
Mladen Bestvina, Mark Feighn (1995)
Inventiones mathematicae
Structure and Regidity in Hyperbolic Groups. I.
E. Rips, Z. Sela (1994)
Geometric and functional analysis
Structure of geodesics in the Cayley graph of infinite Coxeter groups
Ryszard Szwarc (2003)
Colloquium Mathematicae
Let (W,S) be a Coxeter system such that no two generators in S commute. Assume that the Cayley graph of (W,S) does not contain adjacent hexagons. Then for any two vertices x and y in the Cayley graph of W and any number k ≤ d = dist(x,y) there are at most two vertices z such that dist(x,z) = k and dist(z,y) = d - k. Allowing adjacent hexagons, but assuming that no three hexagons can be adjacent to each other, we show that the number of such intermediate vertices at a given distance from x and y...
Surfaces in the complex projective plane and their mapping class groups.
Hirose, Susumu (2005)
Algebraic & Geometric Topology
Surgery and involutions on 4-manifolds.
Krushkal, Vyacheslav S. (2005)
Algebraic & Geometric Topology
Symmetric knots and the cabling conjecture.
E. Luft, X. Zhang (1994)
Mathematische Annalen
Systolic groups acting on complexes with no flats are word-hyperbolic
Piotr Przytycki (2007)
Fundamenta Mathematicae
We prove that if a group acts properly and cocompactly on a systolic complex, in whose 1-skeleton there is no isometrically embedded copy of the 1-skeleton of an equilaterally triangulated Euclidean plane, then the group is word-hyperbolic. This was conjectured by D. T. Wise.
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