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arXiv · 1806.10108

Motivic Euler characteristics and Witt-valued characteristic classes

Marc Levine
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Abstract

This paper examines a number of related questions about Euler characteristics and characteristic classes with values in Witt cohomology. We establish a motivic version of the Becker-Gottllieb transfer, generalizing a construction of Hoyois. Ananyevskiy's splitting principle reduces questions about characteristic classes of vector bundles in $\text{SL}$-oriented, $\eta$-invertible theories to the case of rank two bundles. We refine the torus-normalizer splitting principle for $\text{SL}_2$ to help compute the characteristic classes in Witt cohomology of symmetric powers of a rank two bundle, and then generalize this to develop a general calculus of characteristic classes with values in Witt cohomology.

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Marc Levine. 2018-06-26. Motivic Euler characteristics and Witt-valued characteristic classes. https://doi.org/10.1017/nmj.2019.6

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