## New answers tagged motivation

9

One of the applications that motivated the development of the theory is the solution of the Segal conjecture which states that the zeroth cohomotopy of a classifying space of a finite group is isomorphic to the completion of the Burnside ring. You can read about this in
G. Carlsson. A survey of equivariant stable homotopy theory. Topology 31 (1992), ...

8

There are many beautiful applications of equivariant topology to combinatorics, via the test map method. I recommend the diploma thesis of Benjamin Matschke as a good place to start reading about this (the test map method is nicely illustrated in Chapter 1).
There are also applications of equivariant cohomology to embedding problems, via the ...

14

Let me give an example of the use of Smith's theory in real algebraic geometry. Smith theory gives a way to compute fixed point sets in terms of equivariant cohomology, for a "modern" treatment see:
Dwyer, William G.; Wilkerson, Clarence W. "Smith theory revisited."
Ann. of Math. (2) 127 (1988), no. 1, 191–198.
Let $M^n_{\mathbb{R}}$ be a smooth manifold ...

Top 50 recent answers are included