What are some good references to learn the foundations of equivariant homotopy theory/algebraic topology, for someone who has a background in basic homotopy theory and a tad more advanced algebraic topology; or a good learning route (e.g. "you have to learn this first" etc.)? If possible, I would like to have the answers contain the main prerequisites of the document (unless they're very explicitly stated at the beginning of the document)

(for instance I don't know anything about spectra, so documents that assume the reader is familiar with them aren't any help, at least for the beginning of the "learning route"; and I only know the definition of model categories, so documents that assume a lot of familiarity with these aren't really helpful either)

My background in this area, which will probably be useful to determine the appropriate documents :

-Basic category theory (Yoneda, limits, colimits, adjunctions, a bit of monoidal and $2$-categories, abelian categories and derived functors in this context, definition and basic properties of quasicategories/$\infty$-groupoids [Kan complexes], definition of model categories)

-Basic algebraic topology (covering space theory, homotopy groups, singular, simplicial and cellular (co)homology, Steenrod operations, basics of spectral sequences like the Atiyah-Hirzebruch spectral sequence, basics on (co)fibrations and weak homotopy equivalences, for topological spaces and simplicial sets)

-Basic group (co)homology (Cup product, transfer, Lyndon-Hichschild-Serre spectral sequence, topological and algebraic interpretations, definition of equivariant cohomology)


1 Answer 1


There's lots of good sources depending on what you particularly want to learn. A decent overview of the theory can be found in these lecture notes.

One of my personal favourites is the book "Transformation Groups and Representation Theory" by tom Dieck.

A really good place to find other references for things (and admittedly where I find most of my reading material) is the nlab page, in your case, have a look at the references section here. You'll see that it even mentions the two sources I have mentioned above.


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .