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

中文翻译：

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关于整数的L谱的同伦类型

我们证明了二次和对称 $\mathrm{大号}$-整数理论与安德森对偶相关，并且两个光谱都整体拆分为 $\mathrm{大号}$实数和广义Eilenberg–Mac Lane谱的理论。结果，我们获得了空间的相应划分$\mathrm{G}/\mathrm{最佳}$。最后，我们证明了最近为研究格洛腾迪克－威特理论而设计的真实L谱的相似结果。