

Spaces with Group Actions

There is a ﬁeld in topology in which people
study spaces with group actions by extending standard
techniques in algebraic topology. When the target
spaces are
manifolds
, such a ﬁeld is often called
transformation groups
. In
this blog post
by Tao, actions of groups on topological spaces are
called dynamical systems.
We usually add the adjective
“equivariant” when we talk about a
variation with group actions. For example, cohomology
theories for spaces with group actions are called
equivariant cohomology theories.
In the world of
spectra
, i.e. in equivariant stable homotopy theory,
the work of May and his collaborators plays a
fundamental role. It is also a basis of
coordinate free spectra
in
[
EKMM97
]
.


