On Betti numbers of certain Sasakian manifolds

Betti numbers of random manifolds

We study mathematical expectations of Betti numbers of configuration spaces of planar linkages, viewing the lengths of the bars of the linkage as random variables. Our main result gives an explicit asymptotic formulae for these mathematical expectations for two distinct probability measures describing the statistics of the length vectors when the number of links tends to infinity. In the proof ...

-betti Numbers of Aspherical Manifolds

Betti Numbers of 3-sasakian Quotients of Spheres by Tori

We give a formula for the Betti numbers of 3-Sasakian manifolds or orbifolds which can be obtained as 3-Sasakian quotients of a sphere by a torus. This answers a question of Galicki and Salamon about the topology of 3-Sasakian manifolds. A (4m+3)-dimensional manifold is 3-Sasakian if it possesses a Riemannian metric with three orthonormal Killing elds deening a local SU(2)-action and satisfying...

Tight Combinatorial Manifolds and Graded Betti Numbers

In this paper, we study the conjecture of Kühnel and Lutz, who state that a combinatorial triangulation of the product of two spheres S×S with j ≥ i is tight if and only if it has exactly i+2j+4 vertices. To approach this conjecture, we use graded Betti numbers of Stanley–Reisner rings. By using recent results on graded Betti numbers, we prove that the only if part of the conjecture holds when ...

On the virtual Betti numbers of arithmetic hyperbolic 3--manifolds

An interesting feature of our argument is that although it uses arithmetic in an essential way, it is largely geometric; in particular there is no use of Borel’s theorem [1]. This makes Theorem 1.1 strictly stronger than [1] in this setting, since no congruence assumptions are made. We recall that a group is said to be large if it has a subgroup of finite index which maps onto a free group of r...