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A filled torus (a doughnut) is a 3-manifold homeomorphic to \(S^1 \times D^2\), where \(D^2\) is the 2-dimensional disk. There exists a deformation retract from the doughnut to a circle, so the fundamental group of the doughnut is \(\pi_1(S^1 \times D^2) \cong \mathbb{Z}\).
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