Nathaniel Stapleton

activity

20202026

collaborators

4 papers

math.AT2026

Partition functors and universal exponential relations

David Mehrle, Millie Rose, Nathaniel Stapleton

We introduce partition functors: algebraic structures indexed by partitions of finite sets and equipped with restriction and transfer maps along refinements. We construct a monad P…

math.AT2026

Composition of bispans of $G$ -sets and plethysm

Nathan Cornelius, Evan Franchere, Usman Hafeez +4

Let $P (G)$ be the Grothendieck ring of the semiring of endomorphisms of the point in the $1$ -category of bispans of finite $G$ -sets for a finite group $G$ . This is the bispan analo…

math.RA2024

On the image of the total power operation for Burnside rings

Nathan Cornelius, Lewis Dominguez, David Mehrle +3

We prove that the image of the total power operation for Burnside rings $A (G) \to A (G ≀ Σ_{n})$ lies inside a relatively small, combinatorial subring $\mathring A(G,n) \subseteq A(G…

math.AT2020

Additive power operations in equivariant cohomology

Peter J. Bonventre, Bertrand J. Guillou, Nathaniel J. Stapleton

Let $G$ be a finite group and $E$ be an $H_{\infty}$ -ring $G$ -spectrum. For any $G$ -space $X$ and positive integer $m$ , we give an explicit description of the smallest Mackey ideal $…

Partition functors and universal exponential relations

Composition of bispans of G-sets and plethysm

On the image of the total power operation for Burnside rings

Additive power operations in equivariant cohomology

Composition of bispans of $G$ -sets and plethysm