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On the homotopy type of L‐spectra of the integers
Journal of Topology  (IF1.582),  Pub Date : 2020-12-27, DOI: 10.1112/topo.12180
Fabian Hebestreit, Markus Land, Thomas Nikolaus

We show that quadratic and symmetric $L$‐theory of the integers are related by Anderson duality and 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.