On the homotopy type of L‐spectra of the integers

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.