External Spanier–Whitehead duality and homology representation theorems for diagram spaces

Lackmann, Malte

doi:10.2140/agt.2023.23.155

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External Spanier–Whitehead duality and homology representation theorems for diagram spaces

Malte Lackmann

Algebraic & Geometric Topology 23 (2023) 155–216

DOI: 10.2140/agt.2023.23.155

Abstract

We construct a Spanier–Whitehead type duality functor relating finite $𝒞$ –spectra to finite $𝒞^{op}$ –spectra and prove that every $𝒞$ –homology theory is given by taking the homotopy groups of a balanced smash product with a fixed $𝒞^{op}$ –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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Volume 23, issue 1 (2023)