94 citations · 195 across the 22 of their papers we have counts for
26 papers
A parametrized Pontryagin--Thom theorem
David Ayala, John Francis
We prove a space-level enhancement of the Pontryagin--Thom theorem, identifying the space of maps from a manifold to a Thom space with a moduli space of submanifolds.
The Tangle Hypothesis: Dimension 1
David Ayala, John Francis
We introduce an -category , the morphisms in which are framed tangles in . We prove that ${\sf Bor…
Symmetries of the cyclic nerve
David Ayala, Aaron Mazel-Gee, Nick Rozenblyum
We undertake a systematic study of the Hochschild homology, i.e. (the geometric realization of) the cyclic nerve, of -categories (and more generally of category-objects…
Symmetries of a rigid braided category
David Ayala, John Francis
We identify natural symmetries of each rigid higher braided category. Specifically, we construct a functorial action by the continuous group on each $\mathcal{E}_{…
Natural symmetries of secondary Hochschild homology
David Ayala, John Francis, Adam Howard
We identify the group of framed diffeomorphisms of the torus as a semi-direct product of the torus with the braid group on 3 strands; we also identify the topological monoid of fra…
Derived Mackey functors and -equivariant cohomology
David Ayala, Aaron Mazel-Gee, Nick Rozenblyum
We establish a novel approach to computing -equivariant cohomology for a finite group , and demonstrate it in the case that . For any commutative ring spectrum $…