On homology covering space and sheaf associated to the homology group

Periodic Cyclic Homology as Sheaf Cohomology

0. Introduction. This paper continues the study of the noncommutative innn-itesimal cohomology we introduced in 3]. This is the cohomology of sheaves on a noncommutative version of the commutative innnitesimal site of Grothendieck ((8]). Grothendieck showed that, for a smooth scheme X of characteristic zero, the cohomology of the structure sheaf on the innnitesimal site gives de Rham cohomol-og...

A Gentle Introduction to Homology, Cohomology, and Sheaf Cohomology

On the Homology Cobordism Group of Homology 3-spheres

In this paper we present our results on the homology cobordism group Θ3Z of the oriented integral homology 3-spheres. We specially emphasize the role played in the subject by the gauge theory including Floer homology and invariants by Donaldson and Seiberg – Witten. A closed oriented 3-manifold Σ is said to be an integral homology sphere if it has the same integral homology as the 3-sphere S. T...

Loop Space Homology Associated to the Mod 2 Dickson Invariants

The spaces BG2 and BDI(4) have the property that their mod 2 cohomology is given by the rank 3 and 4 Dickson invariants respectively. Associated with these spaces one has for q odd the classifying spaces of the finite groups BG2(q) and the exotic family of classifying spaces of 2-local finite groups BSol(q). In this article we compute the loop space homology of BG2(q) ∧ 2 and BSol(q) for all od...

Group actions on homology spheres

This can be stated in a more symmetric manner. Let r be any positive integer not equal to 3. Then n acts freely and homologically trivially on Z r i ff n acts freely and homologically trivially on SL In fact, there is a one-to-one correspondence between such actions on U and such actions on S r. (The classification of such actions is discussed in w In addition the actions constructed have the p...