The Milgram non-operad
C. Berger claimed to have constructed an -operad-structure on the permutohedras, whose associated monad is exactly the Milgram model for the free loop spaces. In this paper I will show that this statement is not correct.
The Milnor-Moore theorem in Tame Homotopy theory.
The minimum number of zeros of Lipschitz-Killing curvature.
The monoid of suspensions and loops modulo Bousfield equivalence
The suspension and loop space functors, Σ and Ω, operate on the lattice of Bousfield classes of (sufficiently highly connected) topological spaces, and therefore generate a submonoid ℒ of the complete set of operations on the Bousfield lattice. We determine the structure of ℒ in terms of a single parameter of homotopy theory which is closely tied to the problem of desuspending weak cellular inequalities.
The multi-morphisms and their properties and applications
In this paper a new class of multi-valued mappings (multi-morphisms) is defined as a version of a strongly admissible mapping, and its properties and applications are presented.
The Mumford conjecture
The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...
The nilpotence and periodicity theorems in stable homotopy theory
The Nilpotent Model for a Function Space
The normalizer of the Weyl group.
The normalizer splitting conjecture for p-compact groups
Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group . We prove that for an odd prime p, the fibration has a section, which is unique up to vertical homotopy.
The Novikov conjecture and low-dimensional topology.
The Primary v...-periodic Family.
The Primitive Elements in MU* K(Z/p, 1).
The Radius of Convergence of Poincaré Series of Loop Spaces.
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 relation between homotopy limits and Bauer's shape singular complex