Hyperhopfian groups and approximate fibrations
Internal functionals and bundle duals.
Local homotopy products
Localization for Hausdorff uniform bundles.
Localization with change of the base space in uniform bundles and sheaves.
Manifold Approximate Fibrations are Approximately Bundles.
Microfibrés et fibrés associés à certaines immersions
More morphisms between bundle gerbes.
Non-associative geometry and discrete structure of spacetime
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
Note on normal sequences of chain complexes
On homotopically regular mappings of manifolds
On inverse limits of (2k+m+1)-disk bundle maps
On properties of approximate fibrations. I.
On the geometric bar construction and the Brown representability theorem
On the surjectivity of shape fibrations
Open subgroups of free topological groups
The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.
Orbit projections as fibrations
The orbit projection of a proper -manifold is a fibration if and only if all points in are regular. Under additional assumptions we show that is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: is a -quasifibration if and only if all points are regular.
Orbit projections of proper Lie groupoids as fibrations
Let be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection is a fibration if and only if is regular.
Poincaré Spaces, Their Normal Fibrations and Surgery.
Quantum classifying spaces and universal quantum characteristic classes
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced and analyzed. Interrelations with the abstract algebraic theory of quantum characteristic classes are discussed. Various non-equivalent approaches to defining universal characteristic classes are outlined.