Some topics concerning homeomorphic parameterizations.
In this survey, we consider several questions pertaining to homeomorphisms, including criteria for their existence in certain circumstances, and obstructions to their existence.
Spherical Fibrations and Manifolds.
-structures and homotopy equivalences.
Splitting Theorems for Certain PD3-Groups.
Splittings of Poincaré Duality Groups.
Sur certaines équivalences d'homotopies
On sait qu’il y a 144 classes d’homotopies d’applications de dans lui-même dont la restriction à est homotope à l’identité: ce sont des exemples d’applications qui induisent l’identité en homologie et en homotopie. Plus généralement, soit un complexe de Poincaré 1-connexe de dimension , qui n’a pas le type d’homotopie rationnelle de : si est formel, nous montrons que le groupe des classes d’homotopies d’applications de dans , dont la restriction au -squelette est homotope à l’identité,...
The cell-like approximation theorem in dimension 5
The cell-like approximation theorem of R. D. Edwards characterizes the n-manifolds precisely as the resolvable ENR homology n-manifolds with the disjoint disks property for 5 ≤ n < ∞. Since no proof for the n = 5 case has ever been published, we provide the missing details about the proof of the cell-like approximation theorem in dimension 5.
The Formal Dimension of a Toplogical Space.
The generalized Schoenflies theorem for absolute suspensions
The aim of this paper is to prove the generalized Schoenflies theorem for the class of absolute suspensions. The question whether the finite-dimensional absolute suspensions are homeomorphic to spheres remains open. Partial solution to this question was obtained in [Sz] and [Mi]. Morton Brown gave in [Br] an ingenious proof of the generalized Schoenflies theorem. Careful analysis of his proof reveals that modulo some technical adjustments a similar argument gives an analogous result for the class...
The geometry of abstract groups and their splittings.
A survey of splitting theorems for abstract groups and their applications. Topics covered include preliminaries, early results, Bass-Serre theory, the structure of G-trees, Serre's applications to SL2 and length functions. Stallings' theorem, results about accessibility and bounds for splittability. Duality groups and pairs; results of Eckmann and collaborators on PD2 groups. Relative ends, the JSJ theorems and the splitting results of Kropholler and Roller on PDn groups. Notions of quasi-isometry,...
The Index of Manifolds with Toral Actions and Geometric Interpretations of the ... (..., (S1, Mn)) Invariant of Atiyah and Singer.
The Relationship between Homology and Topological Manifolds via Homology Transversaltiy
The Topological Version of Groups Generated by Reflections.
The Universal Smooth Surgery Class.
Three-Dimensional Poincaré Duality Groups Which Are Extensions.
Topology and dimension of stable planes: On a conjecture of H. Freudenthal.
Toroidal decompositions of and a family of 3-dimensional ANR’s (AR’s)
Transversality Theories at Dimension Four.
Trivializing Sperical Fibrations and Embeddings of Poincaré Complexes.
Variétés d'orbites