# Hermitian K-theory for stable $\infty$-categories II: Cobordism categories and additivity

@article{Calms2020HermitianKF, title={Hermitian K-theory for stable \$\infty\$-categories II: Cobordism categories and additivity}, author={Baptiste Calm{\`e}s and Emanuele Dotto and Yonatan Harpaz and Fabian Hebestreit and Markus Land and Kristian Jonsson Moi and Denis Nardin and Thomas Nickelsen Nikolaus and Wolfgang Steimle}, journal={arXiv: K-Theory and Homology}, year={2020} }

We define Grothendieck-Witt spectra in the setting of Poincare $\infty$-categories and show that they fit into an extension with a L- and an L-theoretic part. As consequences we deduce localisation sequences for Verdier quotients, and generalisations of Karoubi's fundamental and periodicity theorems for rings in which 2 need not be invertible. Our set-up allows for the uniform treatment of such algebraic examples alongside homotopy-theoretic generalisations: For example, the periodicity theorem…

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