I have a problem understanding the following statement:
If i consider the inclusion $i: \mathbb{C}^* \hookrightarrow \mathbb{C}$ and the universal covering $p: \mathbb{C} \twoheadrightarrow \mathbb{C}^*$ and coordinate functions $z$ and $t$ with $p=z \circ p = e^{2 \pi i t}$ then $p$ induces a maps of graduate algebras $$M^*_{\mathbb{C}^*} \overset{\delta p}{\rightarrow} M^*_{\mathbb{C}}$$ $$\Omega^*_{\mathbb{C}^*} \overset{\delta p}{\rightarrow} \Omega^*_{\mathbb{C}}$$ where $M^*_{\mathbb{C}^*}, \Omega^*_{\mathbb{C}^*}$ are the meromorphic and holomorphic differential forms on $\mathbb{C}$ and $\delta p \vert_{\mathcal{O}_{\mathbb{C}^*}}=p^*$
Well, the inclusion is just $\tilde{z}\mapsto \tilde{z}$ and the universal covering of $\mathbb{C}^*$ is given by the exponential $\tilde{z} \mapsto e^{\tilde{z}}$. The decktransformation for this cover are the multiplication with the roots of unity. So I can get maps $z$ and $t$ s.th. $p=z(p)=z(p(t))=e^{2 \pi i t}$. Also the holomorphic (meromorphic resp.) functions on $\mathbb{C}$ are $\mathcal{O}_{\mathbb{C}} = \Omega^0_{\mathbb{C}} \subset M^0_{\mathbb{C}} = \mathcal{M}_{\mathbb{C}}$. Therefore I get inclusions
$$\Omega^*_{\mathbb{C}} \hookrightarrow M^*_{\mathbb{C}}$$ $$\Omega^*_{\mathbb{C}^*} \hookrightarrow M^*_{\mathbb{C}^*}$$
But I dont understand, where this map $\delta p$ comes from, and especially what it does on differential forms. In the statement it also restricts $p$ to the pull-back.