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 rational homotopy theory of smooth, complex projective varieties
The rational homotopy type of configuration spaces of two points
We prove that the rational homotopy type of the configuration space of two points in a -connected closed manifold depends only on the rational homotopy type of that manifold and we give a model in the sense of Sullivan of that configuration space. We also study the formality of configuration spaces.
The real K-ring of some CW-complexes of small dimension
The Reidemeister trace and the calculation of the Nielsen number
The relation between homotopy limits and Bauer's shape singular complex
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 ring of upper triangular invariants as a module over the Dickson invariants.
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.
The Salvetti complex and the little cubes
For a real central arrangement , Salvetti introduced a construction of a finite complex Sal which is homotopy equivalent to the complement of the complexified arrangement in [Sal87]. For the braid arrangement , the Salvetti complex Sal serves as a good combinatorial model for the homotopy type of the configuration space of points in , which is homotopy equivalent to the space of k little -cubes. Motivated by the importance of little cubes in homotopy theory, especially in the study of...
The Section Problem and the Lifting Problem.
The semi-index product formula
We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and .
The set of paths in a space and its algebraic structure. A historical account
The present paper provides a test case for the significance of the historical category “structuralism” in the history of modern mathematics. We recapitulate the various approaches to the fundamental group present in Poincaré’s work and study how they were developed by the next generations in more “structuralist” manners. By contrasting this development with the late introduction and comparatively marginal use of the notion of fundamental groupoid and the even later consideration of equivalence relations...
The set of rational homotopy types with given cohomology algebra.
The shape genus of a shape map
The shape of a category up to directed homotopy.
The shape of a group---connections between shape theory and the homology of groups
The shape of a map
The sigma orientation for analytic circle-equivariant elliptic cohomology.