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Let $g$ and $n$ be positive integers such that $3g-3 + n > 0$ Let $\mathcal{M}_{g,n}$ the moduli stack of genus $g$ nodal curves with $n$ marked points. There are two obvious families of maps

forgetting a point

$$\mathcal{M}{g,n+1} $\mathcal{M}_{g,n+1} \rightarrow \mathcal{M}{}{g,n}$$mathcal{M}_g{}_n$$

and identifying two marked points

$$\mathcal{M}_{g_1,n_1} \times \mathcal{M}_{g_2,}{}_{n_2} \rightarrow \mathcal{M}_{g_1 + g_2,}{}_{n_1 + n_2 - 2}$$

This system constitutes the so-called Grothendieck-Teichmüller tower. It is indeed intricate and in my opinion, also beautiful. Moreover, it is a conjecture of Grotehndieck that its automorphism group is naturally isomorphic to the absolute Galois group over $\mathbb{Q}$.
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Let $g$ and $n$ be positive integers such that $3g-3 + n > 0$ Let $\mathcal{M}_{g,n}$ the moduli stack of genus $g$ nodal curves with $n$ marked points. There are two obvious families of maps

forgetting a point

$$\mathcal{M}_{g,n+1} $\mathcal{M}{g,n+1} \rightarrow \mathcal{M}_g{}_n$$mathcal{M}{}{g,n}$$

and identifying two marked points

$$\mathcal{M}_{g_1,n_1} \times \mathcal{M}_{g_2,}{}_{n_2} \rightarrow \mathcal{M}_{g_1 + g_2,}{}_{n_1 + n_2 - 2}$$

This system constitutes the so-called Grothendieck-Teichmüller tower. It is indeed intricate and in my opinion, also beautiful. Moreover, it is a conjecture of Grotehndieck that its automorphism group is naturally isomorphic to the absolute Galois group over $\mathbb{Q}$.
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Let $g$ and $n$ be positive integers such that $3g-3 + n > 0$ Let $\mathcal{M}_{g,n}$ the moduli stack of genus $g$ nodal curves with $n$ marked points. There are two obvious families of maps

forgetting a point

$$\mathcal{M}_{g,n+1} \rightarrow \mathcal{M}_g{}_n$$

and identifying two marked points

$$\mathcal{M}_{g_1,n_1} \times \mathcal{M}_{g_2,}{}_{n_2} \rightarrow \mathcal{M}_{g_1 + g_2,}{}_{n_1 + n_2 - 2}$$

This system constitutes the so-called Grothendieck-Teichmüller tower. It is indeed intricate and in my opinion, also beautiful. Moreover, it is a conjecture of Grotehndieck that its automorphism group is naturally isomorphic to the absolute Galois group over $\mathbb{Q}$.