Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem

Alexander Kupers; Bena Tshishiku; Jeffrey Giansiracusa

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Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem

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arxiv 1907.07782 v2 pith:K7ACEWNS submitted 2019-07-17 math.AT math.GTmath.KT

Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem

Jeffrey Giansiracusa , Alexander Kupers , Bena Tshishiku This is my paper

classification math.AT math.GTmath.KT

keywords bundlesclassesdiffmethodsprovearithmeticauthorborel

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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.

Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem

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