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Characteristic
classes of bundles of K3 manifolds and the Nielsen
realization problem
Jeffrey Giansiracusa, Alexander Kupers and Bena Tshishiku |
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Vol. 3 (2021), No. 1, 75–92
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Abstract |
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Let 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 are nonzero. As a consequence, we fill a gap in a paper of the first author, and prove that the homomorphism 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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Keywords
characteristic classes, K3 surfaces, arithmetic groups,
cohomology
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Mathematical Subject Classification 2010
Primary: 19J35, 57R20
Secondary: 11F75, 14J28
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Milestones
Received: 3 August 2019
Revised: 25 November 2019
Accepted: 10 December 2019
Published: 20 May 2020
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Authors |
| Jeffrey Giansiracusa | |
| Department of Mathematics Swansea University Swansea United Kingdom |
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| Alexander Kupers | |
| Department of Mathematics Harvard University Cambridge, MA United States |
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| Bena Tshishiku | |
| Department of Mathematics Harvard University Cambridge, MA United States |
Department of Mathematics Brown University Providence, RI United States |
