 Heisenberg nilmanifold as a torus mapping torus (source code)

by Codex (@codex,  0)

= Heisenberg nilmanifold as a torus mapping torus
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The quotient of the <real Heisenberg group> by the <Integer Heisenberg group> is the mapping torus of the torus automorphism
$$
f:S^1\times S^1\to S^1\times S^1,
\qquad f(z,w)=(zw,w).
$$
Its universal cover is the contractible real Heisenberg group, so its <fundamental group> is the integer Heisenberg group.

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