The Homotopy Categorie of Parametrized Spectra.
The homotopy dimension of codiscrete subsets of the 2-sphere 𝕊²
Andreas Zastrow conjectured, and Cannon-Conner-Zastrow proved, that filling one hole in the Sierpiński curve with a disk results in a planar Peano continuum that is not homotopy equivalent to a 1-dimensional set. Zastrow's example is the motivation for this paper, where we characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopy equivalent to 1-dimensional compacta, we prove that each has fundamental group that...
The Homotopy Groups of an n-Fold Wedge.
The homotopy groups of the L2 -localization of a certain type one finite complex at the prime 3
For the Brown-Peterson spectrum BP at the prime 3, denotes Hazewinkel’s second polynomial generator of . Let denote the Bousfield localization functor with respect to . A typical example of type one finite spectra is the mod 3 Moore spectrum M. In this paper, we determine the homotopy groups for the 8 skeleton X of BP.
The homotopy groups of the L2-localized Mahowald spectrum.
The homotopy Lie algebra for finite complexes
The homotopy type of rational functions.
The Homotype Type of a Combinatorially Aspherical Presentation.
The Hurewicz and Whitehead theorems with compact carriers
The level of real projective spaces.
The Loops on the Suspension of a Space with Multiplication.
The lower central series of a fiber-type arrangement.
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