منابع مشابه
Cracks in topological rigidity
Topological rigidity is an analogue of the Baum-Connes conjecture, and is motivated by Mostow rigidity and Margulis superrigidity. I will discuss some of the places where this heuristic reasoning fails, and the rigidity shows some cracks – that are rather different than the places where strong forms of the Baum-Connes conjecture fails.
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Let M be a complete Riemannian manifold having constant sectional curvature —1 and finite volume. Let M denote its Gromov-Margulis manifold compactification and assume that the dimension of M is greater than 5. (If M is compact, then M = M and dM is empty.) We announce (among other results) that any homotopy equivalence h: (N,dN) —• (M,dM), where N is a compact manifold, is homotopic to a homeo...
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A projective algebraic surface which is homeomorphic to a ruled surface over a curve of genus g ≥ 1 is itself a ruled surface over a curve of genus g. In this note, we prove the analogous result for projective algebraic manifolds of dimension 4 in case g ≥ 2.
متن کاملOpen Problems in Rigidity
A collection of open problems that were described in or arose from the problem session in Lancaster on June 5th 2016. The problems are listed in the order they were sent to me. If you would like to add a problem to the list then please e-mail me.
متن کاملA Topological Analogue of Mostow's Rigidity Theorem
Three types of manifolds, spherical, fiat, and hyperbolic, are paradigms of geometric behavior. These are the Riemannian manifolds of constant positive, zero, and negative sectional curvatures, respectively. (The positive and negative sectional curvatures may be assumed, after scaling, to be + 1 and -1.) There is an equivalent synthetic geometric definition of them in terms of coordinate charts...
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ژورنال
عنوان ژورنال: Journal of Advanced Studies in Topology
سال: 2016
ISSN: 2090-388X,2090-8288
DOI: 10.20454/jast.2016.1095