I was reading the book here, and in 2.1.11, there is a diagram which involves an arrow looking like this: $$ H^0_{\mathrm{dR}}(M) \hookrightarrow \Omega^0(M)/\Omega^0_{\text{cl}}(M)_{\mathbb{Z}} $$ where $M$ is a smooth mfld, $H_{\mathrm{dR}}$ is de Rham cohomology, the "cl" subscript denotes closed forms, and the $\mathbb{Z}$ subscript denotes (in this case) locally-constant $\mathbb{Z}$-valued functions on $M$. (In general it denotes integral periods.)
I presume the map is the obvious one sending a 0th de Rham class, viewed as a locally constant real function (not modulo anything), to the function's class modulo the locally constant integer-valued functions.
The hooked arrow suggests the map is injective. However, I don't see why this is: a function which is locally-constant and $\mathbb{Z}$-valued, is not necessarily everywhere zero (which is necessary for it to be trivial in $H^0_{\text{dR}}$). Is this a typo?