Place: N820
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Place: N820
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Place: N820
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Place: N820
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Place: N820
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Place: N820
Title: On the simplest simply connected non-spin rational homology 7-spheres that are not 2-connected
Abstract: Rational homology spheres occupy a distinguished position in topology, encoding torsion phenomena. In low dimensions they already play an important role, and in higher dimensions they provide a testing ground for surgery theory and manifold classification. For simply connected cases, the classification is well understood in dimensions five and six, whereas dimension seven exhibits much richer topology. This is reflected in Milnor’s λ-invariant, originally defined for homotopy 7-spheres, detecting exotic smooth structures on the 7-sphere and extending to all rational homology 7-spheres. In this talk, we classify the simplest non-spin non-2-connected cases, showing that these manifolds are completely determined by the λ-invariant.
Place: N820
Title: An almost flat spinc manifold bounds
Abstract: We prove that every almost flat spinc manifold bounds a compact orientable manifold, thereby settling, in the spinc case, a long-standing conjecture of Farrell-Zdravkovska and S. T. Yau. This is a joint work with Fei Han and Weiping Zhang.