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AG Seminar - 19.23.23

Luciana Basualdo Bonatto - Decoupling Moduli of Configurations Spaces on Surfaces

Abstract: The study of topological field theories and topological bordism categories have motivated over the last decades a quest to understand moduli spaces of manifolds. Many successful techniques have been applied to understand these spaces such as homological stability. Inspired by factorization homology and generalized categories of cobordisms, where manifolds can have punctures or singularities, we look at a generalized moduli space construction. In this talk, we will discuss how these can be constructed as moduli of configuration spaces on manifolds and we will use such description to obtain results such as homological stability. This can be interpreted as a Diff-equivariant homological stability for factorization homology. We will show that such results follow from a decoupling theorem for these moduli spaces with configurations in the case of surfaces: in a range, their homology is completely described by the product of the moduli space of surfaces and a generalized configuration space of points in the infinite Euclidean space.