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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

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