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Proceedings of the American Mathematical Society

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Some hermitian K-groups via geometric topology


Authors: Manuel Krannich and Alexander Kupers
Journal: Proc. Amer. Math. Soc. 149 (2021), 2745-2752
MSC (2020): Primary 19G38, 57S05, 55P47
DOI: https://doi.org/10.1090/proc/15098
Published electronically: April 22, 2021
MathSciNet review: 4257790
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Abstract: We compute the first two symplectic quadratic K-theory groups of the integers, or equivalently, the first two stable homology groups of the group of symplectic integral matrices preserving the standard quadratic refinement. The main novelty in our calculation lies in its method, which is based on high-dimensional manifold theory.


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Additional Information

Manuel Krannich
Affiliation: Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
MR Author ID: 1345715
ORCID: 0000-0003-1994-5330
Email: krannich@dpmms.cam.ac.uk

Alexander Kupers
Affiliation: Department of Computer and Mathematical Sciences, University of Toronto Scarborough, 1265 Military Trail, Toronto, ON M1C 1A4, Canada
MR Author ID: 1053091
Email: a.kupers@utoronto.ca

Received by editor(s): October 28, 2019
Received by editor(s) in revised form: February 29, 2020, and March 14, 2020
Published electronically: April 22, 2021
Additional Notes: The first author was supported by O. Randal-Williams’ Philip Leverhulme Prize from the Leverhulme Trust and by the ERC under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 756444).
The second author was supported by NSF grant DMS-1803766.
Communicated by: Mark Behrens
Article copyright: © Copyright 2021 American Mathematical Society