We determine a nice simple formula for the largest Euclidean space which there is an orientable n -manifold with nonimmersion detected by Stiefel-Whitney classes. For Spin manifolds, we prove analogue of upper bound and establish complete answer ≤ 23 32 33 . Results similar to many these were obtained some 50 years ago, but in much less tractable form. The sharp results manifolds require detail...

We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW-complexes with the homotopy type of an Eilenberg-MacLane space K(π, 1) equipped with a cellular self-map of prime order. As an application we derive the section conjecture for the real points of aspherical varieties defined over the field of real numbers and the natural an...

The sectional category of a subgroup inclusion H↪G can be defined as the corresponding map between Eilenberg–MacLane spaces. We extend characterization topological complexity aspherical spaces given by Farber, Grant, Lupton and Oprea to context inclusions investigate it means Adamson cohomology theory.

We show that for closed orientable manifolds the k-dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree k that generate cohomology in top-degree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles of dimension at least two. Additionally, we prove that the stable systolic const...

Large scale phenomena in homotopy theory (Jordan Hall 124) Paul Goerss (Northwestern University) In the late 1940s it wasn’t clear which was the harder problem: the cohomology of Eilenberg-MacLane spaces or the stable homotopy groups of spheres. After the Cartan-Serre work on Eilenberg-MacLane spaces in the early ’50s, people then optimistically set about computing the homotopy groups of sphere...

The natural transformation Ξ from L–theory to the Tate cohomology of Z/2 acting on K–theory (constructed in [WW2] and [WW3]) commutes with external products. Corollary: The Tate cohomology of Z/2 acting on the K–theory of any ring with involution is a generalized Eilenberg–MacLane spectrum, and it is 4–periodic.

Abstract Let Q denote the cyclic group of order two. Using Tate diagram we compute RO ( )-graded coefficients Eilenberg–MacLane -spectra and describe their structure as modules over spectrum Burnside Mackey functor. If underlying functor is a Green functor, also obtain multiplicative on coefficients.

An enrichment of a category of Dieudonné modules is made by considering Yang–Baxter conditions, and these are used to obtain ring and coring operations on the corresponding Hopf algebras. Some examples of these induced structures are discussed, including those relating to the Morava K-theory of Eilenberg–MacLane spaces.

The natural transformation Ξ from L–theory to the Tate cohomology of Z/2 acting on K–theory (constructed in [WW2] and [WWd]) commutes with external products. Corollary: The Tate cohomology of Z/2 acting on the K–theory of any ring with involution is a generalized Eilenberg–MacLane spectrum, and it is 4–periodic.

In an earlier paper of Čadek, Vokř́ınek, Wagner, and the present authors, we investigated an algorithmic problem in computational algebraic topology, namely, the computation of all possible homotopy classes of maps between two topological spaces, under suitable restriction on the spaces. We aim at showing that, if the dimensions of the considered spaces are bounded by a constant, then the comput...