The rank of actions on -trees
The rank of vector fields of Grassmannian manifolds
The rational homotopy of Thom spaces and the smoothing of homology classes.
The rational homotopy of Thom spaces and the smoothing of isolated singularities
Rational homotopy methods are used for studying the problem of the topological smoothing of complex algebraic isolated singularities. It is shown that one may always find a suitable covering which is smoothable. The problem of the topological smoothing (including the complex normal structure) for conical singularities is considered in the sequel. A connection is established between the existence of certain relations between the normal Chern degrees of a smooth projective variety and the question...
The real genus of the alternating groups.
The recognition problem for topological manifolds
The reduction of quantum invariants of 4-thickenings
We study the sensibility of an invariant of 2-dimensional CW complexes in the case when it comes as a reduction (through a change of ring) of a modular invariant of 4-dimensional thickenings of such complexes: it is shown that if the Euler characteristic of the 2-complex is greater than or equal to 1, its invariant depends only on homology. To see what is happening when the Euler characteristic is smaller than 1, we use ideas of Kerler and construct, from any tortile category, an invariant of 4-thickenings...
The reflexible hypermaps of characteristic
The regular open-open topology for function spaces.
The regular projective solution space of the figure-eight knot complement.
The Reidemeister-Turaev torsion of standard Spin structures on Seifert fibered 3-manifolds
The Reidemeister-Turaev torsion is an invariant of 3-manifolds equipped with Spin structures. Here, a Spin structure of a 3-manifold is a homology class of non-singular vector fields on it. Each Seifert fibered 3-manifold has a standard Spin structure, which is represented as a non-singular vector field the set of whose orbits give a Seifert fibration. We provide an algorithm for computing the Reidemeister-Turaev torsion of the standard Spin structure on a Seifert fibered 3-manifold. The machinery...
The Relationship between Homology and Topological Manifolds via Homology Transversaltiy
The relative coincidence Nielsen number
We define a relative coincidence Nielsen number for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing by the ordinary Nielsen numbers.
The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces
The representation theory and the branching graph for the family of Turaev algebras .
The representation theory of the Temperley-Lieb algebras.
The rhombic dodecahedron and semisimple actions of Aut(Fₙ) on CAT(0) spaces
We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fₙ) has a fixed point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated ℤ⁴ ⊂ Aut(F₃) leaves invariant an isometrically embedded copy of Euclidean 3-space 𝔼³ ↪ X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet...
The Rhombidodecahedral Tessellation of 3-Space and a Particular 15-Vertex Triangulation of the 3-Dimensional Torus.
The Ricci tensor of an almost homogeneous Kähler manifold.
The S1-CW decomposition of the geometric realization of a cyclic set
We show that the geometric realization of a cyclic set has a natural, -equivariant, cellular decomposition. As an application, we give another proof of a well-known isomorphism between cyclic homology of a cyclic space and -equivariant Borel homology of its geometric realization.