We propose a new type of state sum model for two-dimensional surfaces that
takes into account topology and spin. The definition used - new to the
literature - provides a rich class of extended models called spin models. Both
examples and general properties are studied. Most prominently, we find this
type of model can depend on a surface spin structure through parity alone and
we explore explicit cases that feature this behaviour. Further directions for
the two dimensional world are analysed: we introduce a source of new
information - defects - and show how they can enlarge the class of spin models
available.Comment: PhD thesis, 149 pages, 19 figure
