Atiyah–Segal completion for the Hermitian K-theory of symplectic groups

Hornbostel, Jens; Rohrbach, Herman; Zibrowius, Marcus

doi:10.2140/agt.2025.25.4037

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Atiyah–Segal completion for the Hermitian K-theory of symplectic groups

Jens Hornbostel, Herman Rohrbach and Marcus Zibrowius

Algebraic & Geometric Topology 25 (2025) 4037–4072

DOI: 10.2140/agt.2025.25.4037

Abstract

We study equivariant Hermitian K-theory for representations of symplectic groups, especially ${SL}_{2}$ . The results are used to establish an Atiyah–Segal completion theorem for Hermitian K-theory and symplectic groups.

Keywords

Hermitian K-theory, Atiyah–Segal completion, motivic homotopy theory, classifying space, symmetric representation ring, acceptable gadget, admissible gadget, Grothendieck–Witt group, symplectic group

Mathematical Subject Classification

Primary: 19G38

References

Publication

Received: 23 November 2023

Revised: 22 October 2024

Accepted: 2 December 2024

Published: 29 October 2025

Authors

Jens Hornbostel
Fakultät IV Mathematik und Informatik Bergische Universität Wuppertal Wuppertal Germany

Herman Rohrbach
Faculty of Mathematics Universität Duisburg-Essen Essen Germany

Marcus Zibrowius
Mathematisches Institut Heinrich Heine University Düsseldorf Düsseldorf Germany

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Volume 25, issue 7 (2025)