On characteristic classes of exotic manifold bundles

Manuel Krannich

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arxiv 1802.02609 v2 pith:K2RPJ2QR submitted 2018-02-07 math.AT math.GT

On characteristic classes of exotic manifold bundles

Manuel Krannich This is my paper

classification math.AT math.GT

keywords sigmabundlescharacteristicclassesconnectedexoticinvertingmanifold

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Given a closed simply connected manifold $M$ of dimension $2n\ge6$, 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 $M\sharp\Sigma$ with an exotic sphere $\Sigma$. We show that, after inverting the order of $\Sigma$ 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 $\Sigma$ is necessary.

On characteristic classes of exotic manifold bundles

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