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Iddo Samet, Hebrew University
Homology and volume of negatively curved orbifolds The idea that volume restricts topological complexity is classical in the study of negatively curved manifolds. In the early 80's Gromov proved that the Betti numbers of a negatively curved manifold are bounded linearly by its volume. We show that this linear bound holds also for negatively curved orbifolds. This implies, for example, that if $\Gamma$ is a lattice (possibly with torsion) in a rank-one Lie group then the rank of its homology with rational coefficients is bounded linearly by its co-volume. ← Back to the seminar home page |