A twisted Version of controlled K-Theory

Abstract

This paper studies controlled operator K−theory on coarse spaces in light of new studies in [2]. Contents

Coarse Cohomology with twisted Coefficients

“…It suffices to show that It would be possible, conversely, after a more thorough examination that coarse (co-)homology theories which are standard tools can be computed using sheaf cohomology tools. By [20] a modified version of controlled K−theory serves as cosheaf homology. As of now we showed coarse cohomology in dimension 2 is a sheaf on coarse spaces.…”

Coarse Cohomology with twisted Coefficients

“…In light of the new cohomology theory we study controlled operator K-theory and compute examples. The first part, Section 4.1 is the same as [13,Chapter 6] and the second part, Section 4.2 is the whole of [14].…”