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On characteristic classes of exotic manifold bundles

Accepted version
Peer-reviewed

Type

Article

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Abstract

Given a closed simply connected manifold M of dimension 2n≥6, we compare the ring of characteristic classes of smooth oriented bundles with fibre M to the analogous ring resulting from replacing M by the connected sum MΣ with an exotic sphere Σ. We show that, after inverting the order of Σ in the group of homotopy spheres, the two rings in question are isomorphic in a range of degrees. Furthermore, we construct infinite families of examples witnessing that inverting the order of Σ is necessary.

Description

Keywords

math.AT, math.AT, math.GT, 55R40, 57R60, 57S05, 55N22

Journal Title

Mathematische Annalen

Conference Name

Journal ISSN

0025-5831
1432-1807

Volume Title

379

Publisher

Springer Science and Business Media LLC

Rights

All rights reserved