7 problems

Arone's conjecture. The category formed by these sections is equivalent to $K(\mathsf{OEpi})$. Moreover, $\mathsf{OEpi}$ is a twisted Koszul self-dual category: $K(\mathsf{OEpi})$…

Product-rule conjecture. There is an equivalence of right $K(\mathsf{OEpi})$-modules

Symmetric monoidality conjecture. For $\mathsf{OEpi}$,

Let $F \colon \mathcal{J} \to \mathcal{S}$ be lax symmetric monoidal, and let $\Theta^1F$ denote its first derivative spectrum. First derivative multiplication conjecture. The spec…

Untwisted multiplication conjecture. The maps constructed from the monoidal structure make $\widetilde{\Theta^n}F$ into a nonunital $E_\infty$-ring spectrum.

Let $\Lcal_n$ be the partition complex, let $\Pcal_n^\diamond$ denote the unreduced suspension of the partition complex associated to the partition lattice, and let…

Let $V$ be a real inner-product space, let $QBE_k^{(\mathbb R\oplus V)\otimes_{\mathbb R}\rho_k}$ denote the source spaces in the Weiss tower, and let $\operatorname{hoNat}$ denote…