Simplicial Methods

Abstract

In this chapter, we introduce simplicial methods that can be used to give concrete realizations for many of the cohomology theories encountered so far. We start with simplicial (co)homology,which is historically the first such theory. It is highly computable, at least in principle, but it suffers the disadvantage of depending on a triangulation. This can be overcome by working with singular (co)homology, which we briefly discuss, since it is the standard approach in topology. Fortunately, for reasonable spaces singular cohomology coincides with sheaf cohomology with constant coefficients. So all is well.