Explore the unique phenomenon of infinite families of homeomorphic but non-diffeomorphic 4-manifolds in this lecture by Danny Ruberman from Brandeis University. Delve into the combination of gauge theory (Seiberg-Witten theory or Yang-Mills theory) and Freedman's topological classification results that demonstrate this distinctive behavior. Discover the joint project with Dave Auckly, which reveals similar 'exotic' characteristics when comparing the topology of diffeomorphism and homeomorphism groups of smooth 4-manifolds. Learn about their main theorem, which proves that the kernel of the map on homotopy groups induced by inclusion can be infinitely generated. Examine how these techniques also yield comparable results for spaces of embeddings of surfaces and 3-manifolds in 4-manifolds.
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Syllabus
Danny Ruberman: Diffeomorphism groups of 4-manifolds
Taught by
IMSA
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