  I present a method of quantization using cohomology groups extended via
coefficient groups of different types. This is possible according to the
Universal Coefficient Theorem (UCT). I also show that by using this method new
features of quantum field theory not visible in the previous treatments emerge.
The main argument is that several constructions considered as absolute until
now may appear as relative, depending on individual choices of group structures
needed to probe a topology. The universal coefficient theorem also gives
information about how these structures as measured by different choices of
groups, relate to each other. This may result in the formulation of new
dualities and a deeper understanding of the relation between quantum field
theories and gravity.
