Structure and Regidity in Hyperbolic Groups. I.
Structure of geodesics in the Cayley graph of infinite Coxeter groups
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.
Surgery and involutions on 4-manifolds.
Symmetric knots and the cabling conjecture.
Systolic groups acting on complexes with no flats are word-hyperbolic
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.
The real genus of the alternating groups.
Toric structures on near-symplectic 4-manifolds
A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on the base of...
Trimming.
Uniformisation en dimension trois
Visualization of the isometry group action on the Fomenko-Matveev-Weeks manifold.
Изометрии гиперболических многообразий Фибоначчи.
Об обобщении групп Фибоначчи
Об отсутствии теорем конечности Альфорса и Сулливана для клейновых групп в высших размерностях.
Оценки числа автоморфизмов римановой поверхности.