The Leray-Schauder index and the fixed point theory for arbitrary ANRs
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 Lyusternik-Shnirel'man category, vector bundles, and immersions of manifolds.
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 minimizing of the Nielsen root classes
Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen...
The minimum number of zeros of Lipschitz-Killing curvature.
The Mod 2 Cohomology Rings of Extra-special 2-groups and the Spinor Groups.
The ...-Module Structure for the Cohomology of Two-Stage Spaces.
The moduli space of n tropically collinear points in Rd.
The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations lying on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of n x d matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension...
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 Morava -Theory Eilenberg-Moore spectral sequence.
The multicores in metric spaces and their application in fixed point theory
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.
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 multiplicative structure of K(n)* (BA4).
Let K(n)*(-) be a Morava K-theory at the prime 2. Invariant theory is used to identify K(n)*(BA4) as a summand of K(n)*(BZ/2 × BZ/2). Similarities with H*(BA4;Z/2) are also discussed.
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 Nielsen coincidence theory on topological manifolds
We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.
The Nielsen product formula for coincidences