2023/01/23 by Andrew Ronan, Ronan, Andrew
Mathematics · #55P60 (Primary) 55P91 55P92 (Secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2301.09691
openalex publication_date 2023/01/23 · openalex created_date 2023/01/26 · openalex updated_date 2026/07/28
We develop the theory of nilpotent G-spaces and their localisations, for G a compact Lie group, via reduction to the non-equivariant case using Bousfield localisation. One point of interest in the equivariant setting is that we can choose to localise or complete at different sets of primes at different fixed point spaces - and the theory works out just as well provided that you invert more primes at K ≤ G than at H ≤ G, whenever K is subconjugate to H in G. We also develop the theory in an unbased context, allowing us to extend the theory to G-spaces which are not G-connected.