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arXiv · 2311.02318

The connecting homomorphism for Hermitian $K$-theory

Tao Huang·Heng Xie
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Abstract

We provide a geometric interpretation for the connecting homomorphism in the localization sequence of Hermitian $K$-theory. As an application, we compute the Hermitian $K$-theory of projective bundles and Grassmannians in the regular case. We provide an explicit basis for Hermitian $K$-theory of Grassmannians, which is indexed by even Young diagrams together with another special class of Young diagrams, that we call $\textit{buffalo-check}$ Young diagrams. To achieve this, we develop pushforwards and pullbacks in Hermitian $K$-theory using Grothendieck's residue complexes, and we establish fundamental theorems for those pushforwards and pullbacks, including base change, projection, and excess intersection formulas.

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Tao Huang, Heng Xie. 2023-11-04. The connecting homomorphism for Hermitian $K$-theory. https://arxiv.org/abs/2311.02318

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