Topological classification of quasitoric manifolds with second Betti number 2

Positive Pinching , Volume and Second Betti Number

Our main theorem asserts that for all odd n ≥ 3 and 0 < δ ≤ 1, there exists a small constant, i(n, δ) > 0, such that if a simply connected n-manifold, M , with vanishing second Betti number admits a metric of sectional curvature, δ ≤ KM ≤ 1, then the injectivity radius of M is greater than i(n, δ).

Quasitoric Manifolds over a Product of Simplices

A quasitoric manifold (resp. a small cover) is a 2ndimensional (resp. an n-dimensional) smooth closed manifold with an effective locally standard action of (S) (resp. (Z2)n) whose orbit space is combinatorially an n-dimensional simple convex polytope P . In this paper we study them when P is a product of simplices. A generalized Bott tower over F, where F = C or R, is a sequence of projective b...

Classification of Simplicial Triangulations of Topological Manifolds

In this note we announce theorems which classify simplicial (not necessarily combinatorial) triangulations of a given topological «-manifold M, n > 7 (> 6 if dM = 0 ) , in terms of homotopy classes of lifts of the classifying map r: M —• BTOP for the stable topological tangent bundle of M to a classifying space BTRIn which we introduce below. The (homotopic) fiber of the natural map ƒ: BTRIn —•...

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