Daniel Ruberman

collaborators

4 papers

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.DG2026

The Conformal Laplacian and Positive Scalar Curvature Metrics on Manifolds with Boundary

Steven Rosenberg, Daniel Ruberman, Jie Xu

We give examples of spin $4$ -manifolds with boundary $(M, \partial M)$ such that the boundary $\partial M$ has a positive scalar curvature metric which cannot be extended to a posit…

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 $S^{4}$ …

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 $Z^{\infty}$ in the higher homotopy and homology groups of the diffeomorphism groups of certain $4$ -manifolds. These spheri…