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Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points

dc.contributor.author Cerbo, LFD
dc.contributor.author Stern, Mark A
dc.date.accessioned 2017-06-01T13:48:30Z
dc.date.available 2017-06-01T13:48:30Z
dc.date.issued 2017-06-01
dc.identifier http://arxiv.org/abs/1704.06354v1
dc.identifier.uri http://hdl.handle.net/10161/14624
dc.description.abstract We derive Price inequalities for harmonic forms on manifolds without conjugate points and with a negative Ricci upper bound. The techniques employed in the proof work particularly well for manifolds of non-positive sectional curvature, and in this case we prove a strengthened Price inequality. We employ these inequalities to study the asymptotic behavior of the Betti numbers of coverings of Riemannian manifolds without conjugate points. Finally, we give a vanishing result for $L^{2}$-Betti numbers of closed manifolds without conjugate points.
dc.subject math.DG
dc.subject math.DG
dc.subject math.GT
dc.title Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points
dc.type Journal article
pubs.author-url http://arxiv.org/abs/1704.06354v1
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Trinity College of Arts & Sciences


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