##### Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem
Let $K$ be the K3 manifold. In this note, we discuss two methods to prove that certain generalized Miller--Morita--Mumford classes for smooth bundles with fiber $K$ are non-zero. As a consequence, we fill a gap in a paper of the first author, and prove that the homomorphism $Diff(K)\to \pi_0 Diff(K)$ does not split. One of the two methods of proof uses a result of Franke on the stable cohomology of arithmetic groups that strengthens work of Borel, and may be of independent interest.
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07/18/19 06:05PM
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mathATb: Jeffrey Giansiracusa, Alexander Kupers, Bena Tshishiku : Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem https://t.co/Ru2S56QoMD https://t.co/dOl7dfJf3M