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Seminar

FHT Program Seminar: Homological Instability in Dimension 4 October 06, 2022 (02:15 PM PDT - 03:00 PM PDT)
Parent Program:
Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Hokuto Konno (University of Tokyo)
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FHT Program Seminar: Homological Instability In Dimension 4

Abstract/Media

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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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FHT Program Seminar: Homological Instability In Dimension 4