Talk:Three dimensional Heisenberg group (Ex)
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This is equivalent to the given presentation of the Heisenberg group. Therefore $M$ is the desired closed, orientable $3$-manifold. | This is equivalent to the given presentation of the Heisenberg group. Therefore $M$ is the desired closed, orientable $3$-manifold. | ||
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Latest revision as of 12:52, 7 January 2019
Let be a torus and let and be generators of . Let be a homeomorphism of the torus such that and (ie. is a Dehn twist.) Let be a torus bundle over with monodromy . Then is an HNN extension of and we can write down a presentation , with stable letter . This is equivalent to the given presentation of the Heisenberg group. Therefore is the desired closed, orientable -manifold.