There are many beautiful applications of equivariant topology to combinatorics, via the test map method. I recommend the [diploma thesis][1] 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 [Haefliger][2]-Shapiro-Wu deleted product construction.


  [1]: http://people.mpim-bonn.mpg.de/matschke/DiplomaThesis.pdf
  [2]: http://retro.seals.ch/digbib/view?rid=comahe-002:1962-1963:37::18