It is conjectured that binary cocyclic matrices are a uniform source of Hadamard matrices. In testing this conjecture, it is useful to have a general method of calculating cocyclic matrices. We present such a method in this paper. The method draws on standard cohomology theory of finite groups. In particular we employ the Universal Coefficient Theorem, which expresses the second cohomology grou...

Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction EG×G X of a proper G-CW -complex X satisfying certain finiteness conditions. In particular we give formulas computing the topological K-(co)homology K∗(BG) and K(BG) up to finite abelian torsion groups. They apply for instance to arithmetic groups, word hyperbolic gr...

We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: • AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. • Simple unital AH algebras with slow dimension growth and real rank zero. • C*-algebras with real rank ...

Introduction Our objectives are topological versions of the Nielsen-Schreier Theorem on subgroups of free groups, and the Kurosh Theorem on subgroups of free products of groups. It is known that subgroups of free topological groups need not be free topological [2, 6, and 9]. However we might expect a subgroup theorem when a continuous Schreier transversal exists, and we give such a result in th...

This paper is devoted to the study of abelian automorphism groups of surfaces and 3-folds of general type over complex number field C. We obtain a linear bound in K3 for abelian automorphism groups of 3-folds of general type whose canonical divisor K is numerically effective, and we improve on Xiao’s results on abelian automorphism groups of minimal smooth projective surfaces of general type. M...

We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dim ≤ n and a surjective UV n−1-map r : Z −→ X having the property that: for every finitely generated abelian group G and every integer k ≥ 2 such that dimG X ≤ k ≤ n we have dimG Z ≤ k and r is G-acyclic, or equivalently: for every simply connected CW-complex K with finitely generated homotopy groups such th...

Let p be a prime. We obtain good bounds for the p-adic sizes of the coefficients of the divided universal Bernoulli number B̂n n when n is divisible by p− 1. As an application, we give a simple proof of Clarke’s 1989 universal von Staudt theorem. We also establish the universal Kummer congruences modulo p for the divided universal Bernoulli numbers for the case (p − 1)|n, which is a new result.

The main object of this paper is to introduce and investigate a subclass U(λ, α, β, k) of normalized analytic functions in the open unit disk ∆, which generalizes the familiar class of uniformly convex functions. The various properties and characteristics for functions belonging to the class U(λ, α, β, k) derived here include (for example) a characterization theorem, coefficient inequalities an...

Suppose one is given a discrete group G, a cocompact proper Gmanifold M , and a G-self-map f : M → M . Then we introduce the equivariant Lefschetz class of f , which is globally defined in terms of cellular chain complexes, and the local equivariant Lefschetz class of f , which is locally defined in terms of fixed point data. We prove the equivariant Lefschetz fixed point theorem, which says th...