3 papers
math.AT2025
Classifying spaces of infinity-sheaves
Daniel Berwick-Evans, Pedro Boavida de Brito, Dmitri Pavlov
We prove that the set of concordance classes of sections of an infinity-sheaf on a manifold is representable, extending a theorem of Madsen and Weiss. This is reminiscent of an h-p…
math.AT2024
An algebro-geometric model for the configuration category
Pedro Boavida de Brito, Geoffroy Horel, Danica KosanoviÄ
Using log-geometry, we construct a model for the configuration category of a smooth algebraic variety. As an application, we prove the formality of certain configuration spaces.
math.AT2024
The torus trick for configuration categories
Pedro Boavida de Brito, Michael S. Weiss
We show that in codimension at least 3, spaces of locally flat topological embeddings of manifolds are correctly modelled by derived spaces of maps between their configuration cate…