Central stability homology
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We give a new categorical way to construct the central stability homology of Putman and Sam and explain how it can be used in the context of representation stability and homological stability. In contrast to them, we cover categories with infinite automorphism groups. We also connect central stability homology to Randal-Williams and Wahl’s work on homological stability. We also develop a criterion that implies that functors that are polynomial in the sense of Randal-Williams and Wahl are centrally stable in the sense of Putman.
Mathematics Subject ClassificationPrimary 55N35 Secondary 18A25 20L05 55T05
The author was supported by the Berlin Mathematical School and the Dahlem Research School. The author also wants to thank Aurélien Djament, Daniela Egas Santander, Reiner Hermann, Henning Krause, Daniel Lütgehetmann, Jeremy Miller, Holger Reich, Steven Sam, Elmar Vogt, Nathalie Wahl, Jenny Wilson for helpful conversations. Special thanks to Reiner Hermann and his invitation to NTNU where the idea for this project was born. The author would also like to thank the anonymous referee for many helpful suggestions and corrections.
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