Cohomological finiteness conditions for Mackey and cohomological Mackey functors

2013/10/23 by Simon St John-Green, John-Green, Simon St
Mathematics · #18G #20J05 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1310.6262

openalex publication_date 2013/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study cohomological finiteness conditions for groups associated to Mackey and cohomological Mackey functors, proving that the cohomological dimension associated to cohomological Mackey functors is always equal to the F-cohomological dimension, and characterising the conditions Mackey-FP_n and cohomological Mackey-FP_n. We show that all finiteness conditions for cohomological Mackey functors are unchanged when considering only the family of p-subgroups, and we characterise cohomological Mackey-FP_n conditions over the finite field \mathbbF_p.

Related

• On the projective dimensions of Mackey functors
• The dominant dimension of cohomological Mackey functors
• On equivalences for cohomological Mackey functors
• Complexity and cohomology of cohomological Mackey functors
• Recovering a cohomological Mackey Functor from its restriction to Sylow subgroups