Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
External Spanier–Whitehead duality and homology representation theorems for diagram spaces

Malte Lackmann

Algebraic & Geometric Topology 23 (2023) 155–216
Abstract

We construct a Spanier–Whitehead type duality functor relating finite 𝒞–spectra to finite 𝒞op –spectra and prove that every 𝒞–homology theory is given by taking the homotopy groups of a balanced smash product with a fixed 𝒞op –spectrum. We use this to construct Chern characters for certain rational 𝒞–homology theories.

Keywords
spaces over a category, $\mathcal{C}$–homology theories, representation theorems, external Spanier–Whitehead duality, Chern character
Mathematical Subject Classification
Primary: 55N91
Secondary: 18A25, 55M05, 55P42, 55P62
References
Publication
Received: 16 December 2020
Revised: 3 September 2021
Accepted: 17 October 2021
Published: 27 March 2023
Authors
Malte Lackmann
Mathematisches Institut
Universität Bonn
Bonn
Germany

Open Access made possible by participating institutions via Subscribe to Open.