|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Natural symmetries of
secondary Hochschild homology
David Ayala, John Francis and Adam Howard |
|
Algebraic & Geometric Topology 24 (2024) 1953–2010
|
 |
Abstract |
|
We identify the group of framed diffeomorphisms of the torus as a semidirect product of the torus with the braid group on three strands; we also identify the topological monoid of framed local diffeomorphisms of the torus in similar terms. It follows that the framed mapping class group is this braid group. We show that the group of framed diffeomorphisms of the torus acts on twice-iterated Hochschild homology, and explain how this recovers a host of familiar symmetries. In the case of cartesian monoidal structures, we show that this action extends to the monoid of framed local diffeomorphisms of the torus. Based on this, we propose a definition of an unstable secondary cyclotomic structure, and show that iterated Hochschild homology possesses such in the cartesian monoidal setting. |
Keywords
factorization homology, isogeny, framings, mapping class
group, moduli of elliptic curves, secondary trace,
secondary K–theory, secondary Chern character, secondary
Hochschild homology, topological cyclic homology, cyclic
homology, cyclic operator, Hochschild homology
|
Mathematical Subject Classification
Primary: 58D05
Secondary: 16E40, 58D27
|
References |
Publication
Received: 15 December 2021
Revised: 13 March 2023
Accepted: 1 April 2023
Published: 16 July 2024
|
Authors |
| David Ayala | |
| Department of Mathematics Montana State University Bozeman, MT United States |
|
| John Francis | |
| Department of Mathematics Northwestern University Evanston, IL United States |
|
| Adam Howard | |
| Department of Mathematics Montana State University Bozeman, MT United States |
|
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
