On the homotopy type of L-spectra of the integers

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.

v4: Corrected an oversight in the third comment following Theorem A; v3: Removed an erroneous (but for the paper irrelevant) remark in the appendix. An erratum is available from the webpages of the authors

References in corpus (3)

• Hermitian K-theory for stable $\infty$-categories II: Cobordism categories and additivity
• Hermitian K-theory for stable $\infty$-categories I: Foundations
• Gauss Sums in Algebra and Topology

Cited by in corpus (4)

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• The family signature theorem
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