On the homotopy type of L‐spectra of the integers

DOI10.1112/TOPO.12180zbMATH Open1484.19008arXiv2004.06889OpenAlexW3017096340MaRDI QIDQ4999732

Thomas Nikolaus, Fabian Hebestreit, Markus Land

Publication date: 2 July 2021

Published in: Journal of Topology (Search for Journal in Brave)

Abstract: We show that quadratic and symmetric L-theory of the integers are related by Anderson duality and show that both spectra split integrally into the L-theory of the real numbers and a generalised Eilenberg-Mac Lane spectrum. As a consequence, we obtain a corresponding splitting of the space G/Top. Finally, we prove analogous results for the genuine L-spectra recently devised for the study of Grothendieck--Witt theory.

Full work available at URL: https://arxiv.org/abs/2004.06889

Mathematics Subject Classification ID

Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Universal coefficient theorems, Bockstein operator (55U20) (L)-theory of group rings (19G24)

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