Speaker: Hokuto Konno

Title: Homological instability for moduli spaces of 4-manifolds

Abstract: We prove that homological stability with respect to connected sums of S^2×S^2 fails for moduli spaces BDiff(X) of simply-connected closed 4-manifolds X. This makes a striking contrast with other dimensions: in all even dimensions except for 4, analogous homological stability for moduli spaces has been established by work of Harer and of Galatius and Randal-Williams. The proof of the above result is based on a characteristic class constructed using the Seiberg-Witten equations. This is joint work with Jianfeng Lin.

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