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This research explores the properties of generalized configuration spaces on surfaces and their homological stability.

Decoupling generalised configuration spaces on surfaces

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This research explores the properties of generalized configuration spaces on surfaces and their homological stability.
Investigated actions of the diffeomorphism group on generalized configuration spaces.
Analyzed homotopy quotients and established a decoupling theorem for surfaces.
Studied group completion of the monoid of moduli spaces of configurations.
Demonstrated that homology on surfaces is described by the product of the moduli space and a generalized configuration space of points in R^∞.
Achieved homological stability as the genus increases, confirming stable homology patterns.
Identified Diff-equivariant homological stability relevant to factorization homology.

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Randomized trial reveals homological stability in generalised configuration spaces on surfaces, highlighting implications for topology.

Luciana Basualdo Bonatto (2026) studied this question.

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