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arXiv · 1908.09553

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

Malte Lackmann
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Abstract

We construct a Spanier-Whitehead type duality functor relating finite $\mathcal{C}$-spectra to finite $\mathcal{C}^{\mathrm{op}}$-spectra and prove that every $\mathcal{C}$-homology theory is given by taking the homotopy groups of a balanced smash product with a fixed $\mathcal{C}^{\mathrm{op}}$-spectrum. We use this to construct Chern characters for certain rational $\mathcal{C}$-homology theories.

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Malte Lackmann. 2019-08-26. External Spanier-Whitehead duality and homology representation theorems for diagram spaces. https://doi.org/10.2140/agt.2023.23.155

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