Sam K. Miller

activity

20232026

most citedEndotrivial complexes

4 citations · 7 across the 8 of their papers we have counts for

collaborators

9 papers

math.RT2026

Permutation twisted cohomology, reduced and immersed

Juan Omar Gómez, Sam K. Miller

In this paper, we introduce a `reduced' form of permutation twisted cohomology as introduced by Balmer--Gallauer and further developed by Miller. This ring is bigraded by a well-ch…

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.RT2026

The classification of integral endotrivial complexes

Juan Omar Gómez, Sam K. Miller

We describe the group of endotrivial complexes, i.e., the Picard group, of the derived category of permutation modules for a finite group over a commutative Noetherian ring. As a r…

math.RT2025

The Euler characteristic of an endotrivial complex

Nadia Mazza, Sam K. Miller

Let $G$ be a finite group and $k$ a field of prime characteristic $p$ . We examine the Lefschetz homomorphism $Λ : E_{k} (G) \to O (T (k G))$ from the group of endotrivial comple…

math.RT2024

On endosplit $p$ -permutation resolutions and Broué's conjecture for $p$ -solvable groups

Sam K. Miller

Endosplit $p$ -permutation resolutions play an instrumental role in verifying Broué's abelian defect group conjecture in numerous cases. We give a new characterization of all endosp…

math.GR2024★ 1 cited

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★ 2 cited

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^…

math.RT2023★ 4 cited

Endotrivial complexes

Sam K. Miller

Let $G$ be a finite group, $p$ a prime, and $k$ a field of characteristic $p$ . We introduce the notion of an endotrivial chain complex of $p$ -permutation $k G$ -modules, which are th…

Permutation twisted cohomology, reduced and immersed

Non-orientable representation spheres

The fusion-stable tom Dieck homomorphism

The classification of integral endotrivial complexes

The Euler characteristic of an endotrivial complex

On endosplit p-permutation resolutions and Broué's conjecture for p-solvable groups

The classification of endotrivial complexes

Relatively endotrivial complexes

Endotrivial complexes

On endosplit $p$ -permutation resolutions and Broué's conjecture for $p$ -solvable groups