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Perfect circle-valued Morse functions on hyperbolic 6-manifolds
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math.GTmath.GR
keywords
hyperboliccircle-valuedexamplemanifoldsmathcalmorseperfectadmits
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abstract
We build the first example of a hyperbolic 6-manifold that admits a perfect circle-valued Morse function, which can be considered as the analogue of a fibration over the circle for manifolds with non-vanishing Euler characteristic. As a consequence, we obtain a new example of a subgroup of a hyperbolic group which is of type $\mathcal{F}_2$ but not $\mathcal{F}_3$.
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