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Investigating Hermitian K-theory in depth: Part 1 by Monodeep Mukherjee #HermitianKtheory

The content discusses two different papers on Hermitian K-theory published on arXiv. The first paper, “The connecting homomorphism for Hermitian K-theory,” is authored by Tao Huang and Heng Xie. It provides a geometric interpretation for the connecting homomorphism in the localization sequence of Hermitian K-theory and computes the Hermitian K-theory of projective bundles and Grassmannians in the regular case. The authors achieve this by developing pushforwards and pullbacks in Hermitian K-theory using Grothendieck’s residue complexes and establishing fundamental theorems for those pushforwards and pullbacks.

The second paper, “Atiyah-Segal completion for the Hermitian K-theory of Symplectic Groups,” is authored by Jens Hornbostel, Herman Rohrbach, and Marcus Zibrowius. It focuses on studying equivariant Hermitian K-theory for representations of symplectic groups, particularly SL2, and uses the results to establish an Atiyah-Segal completion theorem for Hermitian K-theory and symplectic groups.

Both papers contribute to the field of Hermitian K-theory by providing new insights and applications of the theory in different contexts. These papers are valuable resources for researchers and scholars interested in Hermitian K-theory and its applications.

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Source link: https://medium.com/@monocosmo77/research-on-hermitian-k-theory-part1-9f6e83d03446?source=rss——artificial_intelligence-5

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Hermitian K-theory research part 2 by Monodeep Mukherjee #HermitianKTheory

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