[[Topology MOC]]
# Torus topology

A **torus** is a [[Topological manifold]] defined as the [[Product topology]] of [[Sphere space|1-spheres]]. #m/def/topology 
$$
\begin{align*}
\mathbb{T}^n = \underbrace{ \mathbb{S}^1 \times \dots \times \mathbb{S}^1 }_{ n }
\end{align*}
$$

## Properties

- Since [[Fundamental group respects products]], the torus fundamental group $\pi_{1}(\mathbb{T}^n)$ of a torus $\mathbb{T}^n$ is $\mathbb{Z}^n$.

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#state/tidy | #lang/en | #SemBr