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arXiv · 2411.06504

KW-Euler Classes via Twisted Symplectic Bundles

Alessandro D'Angelo
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Abstract

In this paper we are going to compute the $ \mathrm{KW} $-Euler classes for rank 2 vector bundles on the classifying stack $ \mathcal{B}N $, where $N$ is the normaliser of the standard torus in $SL_2$ and $\mathrm{KW}$ represents Balmer's derived Witt groups. Using these computations we will recover, through a new and different strategy, the formulas previously obtained by Levine in Witt-sheaf cohomology. In order to obtain our results, we will prove K\"unneth formulas for products of $GL_n$'s and $SL_n$'s classifying spaces and we will develop from scratch the basic theory of twisted symplectic bundles with their associated twisted Borel classes in $SL$-oriented theories.

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Alessandro D'Angelo. 2024-11-10. KW-Euler Classes via Twisted Symplectic Bundles. https://arxiv.org/abs/2411.06504

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