Pathological Computations of Mackey Functor-valued Tor over Cyclic Groups
Algebraic Topology
2025-07-15 v2
Abstract
We compute Mackey functor-valued Tor over certain free incomplete Tambara functors, generalizing the computation of Tor over a polynomial ring on one generator. In contrast with the classical situation where the resulting Tor groups vanish above degree one, we present examples where Tor is nonvanishing in almost every degree. We also discuss a 2-primary analogue of the odd-primary Koszul complexes defined in our other work \cite{MQS24a}.
Cite
@article{arxiv.2410.11974,
title = {Pathological Computations of Mackey Functor-valued Tor over Cyclic Groups},
author = {David Mehrle and J. D. Quigley and Michael Stahlhauer},
journal= {arXiv preprint arXiv:2410.11974},
year = {2025}
}
Comments
v2: Removed section on computations over small cyclic 2-groups; revised in response to referee comments. To appear in the Bulletin of the London Mathematical Society. v1: 16 Pages, 3 Figures. Comments welcome!