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Ideal simplicial volume of manifolds with boundary. (arXiv:1802.05223v1 [math.GT])
来源于:arXiv
We define the ideal simplicial volume for compact manifolds with boundary.
Roughly speaking, the ideal simplicial volume of a manifold $M$ measures the
minimal size of possibly ideal triangulations of $M$ "with real coefficients",
thus providing a variation of the ordinary simplicial volume defined by Gromov
in 1982, the main difference being that ideal simplices are now allowed to
appear in representatives of the fundamental class.
We show that the ideal simplicial volume is bounded above by the ordinary
simplicial volume, and that it vanishes if and only if the ordinary simplicial
volume does. We show that, for manifolds with amenable boundary, the ideal
simplicial volume coincides with the classical one, whereas for hyperbolic
manifolds with geodesic boundary it can be strictly smaller. We compute the
ideal simplicial volume of an infinite family of hyperbolic $3$-manifolds with
geodesic boundary, for which the exact value of the classical simplicial volume
is not known, and we exhi 查看全文>>