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Jun, 2019
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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 ] .

References