T-homotopy and refinement of observation. III. Invariance of the branching and merging homologies.
Top-Dimensional Group of the Basic Intersection Cohomology for Singular Riemannian Foliations
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does not satisfy...
Topological bar-codes of fractals: a new characterization of symmetric binary fractal trees
The goal of this paper is to provide foundations for a new way to classify and characterize fractals using methods of computational topology. The fractal dimension is a main characteristic of fractal-like objects, and has proved to be a very useful tool for applications. However, it does not fully characterize a fractal. We can obtain fractals with the same dimension that are quite different topologically. Motivated by techniques from shape theory and computational topology, we consider fractals...
Topological -theory of the integers at the prime 2.
Topological Order Complexes and Resolutions of Discriminant Sets
Topological order complexes and resolutions of discriminant sets.
Topology and dimension of stable planes: On a conjecture of H. Freudenthal.
Topology of arrangements and position of singularities
This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees)...
Topos based homology theory
In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the interval based homotopies and, for toposes, the excisions represented by “cutting out” subobjects. The...
Torsion in equivariant cohomology.
Torsion in graph homology
Khovanov homology for knots has generated a flurry of activity in the topology community. This paper studies the Khovanov type cohomology for graphs with a special attention to torsion. When the underlying algebra is ℤ[x]/(x²), we determine precisely those graphs whose cohomology contains torsion. For a large class of algebras, we show that torsion often occurs. Our investigation of torsion led to other related general results. Our computation could potentially be used to predict the Khovanov-Rozansky...
Torsion in Milnor fiber homology.
Torsion in one-term distributive homology
The one-term distributive homology was introduced in [Prz] as an atomic replacement of rack and quandle homology, which was first introduced and developed by Fenn-Rourke-Sanderson [FRS] and Carter-Kamada-Saito [CKS]. This homology was initially suspected to be torsion-free [Prz], but we show in this paper that the one-term homology of a finite spindle may have torsion. We carefully analyze spindles of block decomposition of type (n,1) and introduce various techniques to compute their homology precisely....
Towards the algebra structure of the Morava k-theory of the orthogonal groups.
Transfer and complex oriented cohomology rings.
Transformation Groups on Cohomology Product of Spheres.
Travaux de Karoubi sur la K-théorie
Travaux de Quillen sur la cohomologie des groupes
Über Algebren stetiger Operatorfunktionen
Über den Symmetriegrad der rational azyklischen kompakten homogenen Räume.