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A RESULT ON RICCI CURVATURE AND THE SECOND BETTI NUMBER
A RESULT RICCI CURVATURE THE SECOND BETTI NUMBER
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2018/4/19
We prove that the second Betti number of a compact Riemannian manifoldvanishes under certain Ricci curved restriction.
The first $L^2$-Betti number and approximation in arbitrary characteristic
First L2-Betti number approximation in prime characteristic Group Theory
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2012/6/19
Let G be a finitely generated group and (G_i) a descending chain of finite index normal subgroups of G. Given a field K, we consider the sequence b_1(G_i;K)/[G:G_i] of normalized first Betti numbers o...
What is the total Betti number of a random real hypersurface?
Betti number random real hypersurface Algebraic Geometry
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2011/9/2
Abstract: We bound from above the expected total Betti number of a high degree random real hypersurface in a smooth real projective manifold. This upper bound is deduced from the equirepartition of cr...
Approximating the first $L^2$-betti number of residually finite groups
residually finite groups math
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2010/11/24
We show that the first $L^2$-betti number of a finitely generated residually finite group can be estimated from below by using ordinary first betti numbers of finite index normal subgroups. As an app...