This is a summary of research which appears in a preprint of the same title. We prove a K-resolution theorem for simply connected CW-complexes K in extension theory in the class of metrizable compacta X. This means that if dimX ≤ K (in the sense of extension theory), n is the first element of N such that G = πn(K) 6= 0, and it is also true that πn+1(K) = 0, then there exists a metrizable compac...

certain algebraic invariants of the integral group ring zg of a group g were introduced and investigated in relation to the problem of extending the farrell-tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. it turns out that the finiteness of these invariants of a group g implies the existence of a generalized farrell-tate cohomology for g whic...

We give a survey on certain results related to the cohomology of projective schemes with coefficients in coherent sheaves. In particular we present results on cohomological patterns, cohomological Hilbert functions and cohomological Hilbert polynomials. Bounding results for Castelnuovo-Mumford regularities, Severi coregularities and cohomological postulation numbers are discussed. Moreover, a n...

This paper is a systematic approach to the construction of coronas (i.e. Higson dominated boundaries at infinity) combable spaces. We introduce three additional properties for combings: properness, coherence and expandingness. Properness condition under which our corona works. Under assumption expandingness, attaching Rips complex yields contractible [Formula: see text]-compact space in sits as...