The p-primary v1-periodic homotopy groups, v −1 1 π∗(X; p), of a topological space X, as defined in [13], are a localization of the portion of the actual homotopy groups of X detected by K-theory. In [10, 4, 6], v−1 1 π∗(X; p) was calculated for classical groups X and primes p in all cases except (SO(n), 2). In this paper we make a first step toward the calculation of v−1 1 π∗(SO(n); 2), which ...

This paper centers around two basic problems of topological coincidence theory. First, try to measure (with the help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. We give a brief (and necessarily very incomplete) survey of some old and ...

The main goal of the present project is to give a sketch of the calculation of the algebraic K-theory of a finite field. Not all the details are developed, but several references are given where detailed proofs may be found. However, the main source of the project is D.J. Benson’s book on ”Representations and Cohomolgy: Cohomolgy of groups and modules” [4]. Section 1 is an introduction to princ...

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to an unexpected result about homeomorphism groups of manifolds. A tool used in the proof is a surjective splitting of the assembly map for Waldhausen’s functor A(X). We also give concrete examples of f...

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to an unexpected result about homeomorphism groups of manifolds. A tool used in the proof is a surjective splitting of the assembly map for Waldhausen’s functor A(X). We also give concrete examples of f...