4 papers
math.AT2026
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.
math.AT2025
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…
math.AT2024
Traces for factorization homology in dimension 1
David Ayala, John Francis
We construct a circle-invariant trace from the factorization homology of the circle $ {\sf trace} \colon \int^α_{{\mathbb S}^1} \\underline{\sf End}(V) \longrightarrow \uno $ asso…
math.AT2024
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…