Pincement du plan hyperbolique complexe
Differential Geometry
2011-03-24 v1 Metric Geometry
Abstract
-cohomology of rank one symmetric spaces of noncompact type is shown to be Hausdorff for values of where this does not follow from curvature pinching. Using the multiplicative structure on -cohomology, it is shown that no simply connected Riemannian manifold with strictly -1/4-pinched sectional curvature can be quasiisometric to complex hyperbolic plane. Unfortunately, the method does not extend to other rank one symmetric spaces.
Keywords
Cite
@article{arxiv.1103.4460,
title = {Pincement du plan hyperbolique complexe},
author = {Pierre Pansu},
journal= {arXiv preprint arXiv:1103.4460},
year = {2011}
}
Comments
39 pages. Manuscript completed in january 2009, with a minor change last fall. Missing: careful proof of quasiisometry invariance of cup-product in L^p cohomology, postponed to a separate paper