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math.GT2026
Exotic aspherical 4-manifolds
Michael Davis, Kyle Hayden, Jingyin Huang +2
We construct closed, aspherical, smooth 4-manifolds that are homeomorphic but not diffeomorphic. These provide counterexamples to a smooth analog of the Borel conjecture in dimensi…
math.GT2025
Exotic families of embeddings
Dave Auckly, Daniel Ruberman
We construct a number of topologically trivial but smoothly non-trivial families of embeddings of 3-manifolds in 4-manifolds. These include embeddings of homology spheres in …
math.GT2025
Families of diffeomorphisms, embeddings, and positive scalar curvature metrics via Seiberg-Witten theory
Dave Auckly, Daniel Ruberman
We construct infinite rank summands isomorphic to in the higher homotopy and homology groups of the diffeomorphism groups of certain -manifolds. These spheri…