Let
denote the cyclic group of
order
. Given a manifold with
a
–action, we can consider its
equivariant Bredon
–graded
cohomology. We develop a theory of fundamental classes for equivariant submanifolds in
–graded cohomology with
constant
–coefficients. We show
the cohomology of any
–surface
is generated by fundamental classes, and these classes can be used to easily
compute the ring structure. To define fundamental classes we are led to study
the cohomology of Thom spaces of equivariant vector bundles. In general,
the cohomology of the Thom space is not just a shift of the cohomology
of the base space, but we show there are still elements that act as Thom
classes, and cupping with these classes gives an isomorphism within a certain
range.
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