Sam K. Miller

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20232026

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math.GR2026

Non-orientable representation spheres

Sam K. Miller

For any finite group, we pose the following question: given an irreducible real representation, is the associated representation sphere non-orientable if and only if the representa…

math.GR2026

The fusion-stable tom Dieck homomorphism

Sam K. Miller

Tornehave and Yalçin proved that the tom Dieck homomorphism, which sends a virtual real representation to a unit of the Burnside ring, is surjective for any $p$ -group $S$ . We prove…

math.GR2024

The classification of endotrivial complexes

Sam K. Miller

Let $G$ be a finite group and $k$ a field of prime characteristic $p$ . We give a complete classification of endotrivial complexes, i.e. determine the Picard group $\mathcal{E}_k(G)…

math.GR2024

Relatively endotrivial complexes

Sam K. Miller

Let $G$ be a finite group and $k$ be a field of characteristic $p > 0$ . In prior work, we studied endotrivial complexes, the invertible objects of the bounded homotopy category $K^…