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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 325, Pages 244–276
DOI: https://doi.org/10.4213/tm4436 (Mi tm4436) 		 
Algebraic and Homological Aspects of Hermitian $K$-Theory

Th. Yu. Popelenskyab

a Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991 Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia
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DOI: https://doi.org/10.4213/tm4436
Abstract: In 1970, S. P. Novikov proposed a systematization of algebraic results of the surgery theory based on the Hamiltonian formalism over rings with involution. His results have had a significant impact on the development of Hermitian analogs of algebraic $K$-theory. This article was written at S. P. Novikov's suggestion and aims to present the current state of research at the interface between the problems of manifold theory and Hermitian $K$-theory of rings with involution.
Keywords: Hermitian $K$-theory, $L$-groups, ring with involution, quadratic form.
Funding agency
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Received: April 2, 2024
Revised: July 4, 2024
Accepted: July 14, 2024
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 325, Pages 230–261
DOI: https://doi.org/10.1134/S0081543824020147
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Th. Yu. Popelensky, “Algebraic and Homological Aspects of Hermitian $K$-Theory”, Geometry, Topology, and Mathematical Physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday, Trudy Mat. Inst. Steklova, 325, Steklov Mathematical Institute of RAS, Moscow, 2024, 244–276; Proc. Steklov Inst. Math., 325 (2024), 230–261
Citation in format AMSBIB
\Bibitem{Pop24}
\by Th.~Yu.~Popelensky
\paper Algebraic and Homological Aspects of Hermitian $K$-Theory
\inbook Geometry, Topology, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 325
\pages 244--276
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4436}
\crossref{https://doi.org/10.4213/tm4436}
\zmath{https://zbmath.org/?q=an:07939072}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 325
\pages 230--261
\crossref{https://doi.org/10.1134/S0081543824020147}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85207476319}
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