J. Francis

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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.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^Î±_{{\mathbb S}^1} \\underline{\sf End}(V) \longrightarrow \uno $ asso…

math.AT2024

The Tangle Hypothesis: Dimension 1

David Ayala, John Francis

We introduce an $(\infty, 1)$ -category $Bord_{1}^{fr} (R^{n})$ , the morphisms in which are framed tangles in $R^{n} \times D^{1}$ . We prove that ${\sf Bor…

math.AT2024

Factorization homology of topological manifolds

David Ayala, John Francis

Factorization homology theories of topological manifolds, after Beilinson, Drinfeld and Lurie, are homology-type theories for topological $n$ -manifolds whose coefficient systems ar…

math.AT2024

Factorization homology of enriched $\infty$ -categories

David Ayala, John Francis, Aaron Mazel-Gee +1

For an arbitrary symmetric monoidal $\infty$ -category $V$ , we define the factorization homology of $V$ -enriched $(\infty, 1)$ -categories over (possibly stratifie…

A parametrized Pontryagin--Thom theorem

Traces for factorization homology in dimension 1

The Tangle Hypothesis: Dimension 1

Factorization homology of topological manifolds

Factorization homology of enriched ∞-categories

Factorization homology of enriched $\infty$ -categories