Speaker
Prof.
Hokuto Konno
(Tokyo)
Description
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 all other even dimensions, where analogous stability has been established by Harer in dimension 2 and by Galatius and Randal-Williams in dimension higher than 4. The proof of the above result is based on a new characteristic class constructed by using 4-dimensional gauge theory. This is joint work with Jianfeng Lin.
