We express the Lyubeznik numbers of the local ring of a complex isolated singularity in terms of Betti numbers of the associated real link.

We study L-Betti numbers for von Neumann algebras, as defined by D. Shlyakhtenko and A. Connes in [1], in the presence of a bi-finite correspondence and proof a proportionality formula.

Upper bounds on the topological Betti numbers of Vietoris-Rips complexes are established, and examples of such complexes with high Betti

We study the existence of closed characteristics on three-dimensional energy manifolds of second-order Lagrangian systems. These manifolds are always noncompact, connected, and not necessarily of contact type. Using the specific geometry of these manifolds, we prove that the number of closed characteristics on a prescribed energy manifold is bounded below by its second Betti number, which is ea...

In this thesis we give a complete description of the syzygies of irreducible, nonsingular, canoncial curves C of genus 9. This includes a collection of all possible Betti tables for C. Moreover a direct correspondence between these Betti tables and the number and types of special linear series on C is given. Especially for Cliff(C) = 3 the curve C is contained in determinantal surface Y on a 4d...

Let M be a finitely generated module over an Artin algebra. By considering the lengths of each module in the minimal projective resolution of M , we obtain its Betti sequence. This sequence must be bounded if M is eventually periodic, but the converse fails to hold in general. We give conditions under which this holds, using techniques from Hochschild cohomology. We also provide a result which ...

where n = dim M and 6» = ith Betti number of M ( = dim of Hi(M; Q)). Thus the geometric property of M having a nonzero vector field is expressed in terms of the algebraic invariant xM. We will discuss extensions of this idea to vector ^-fields, fields of ^-planes, and foliations of manifolds. All manifolds considered will be connected, smooth and without boundary; all maps will be continuous. F...

We show that the first betti number b1 (0) = d im H 1(0, !R) of a compact Riemannian orbifold 0 with Ricci curvature Ric(O ) ~ -(n 1)k and d iameter diam(O) :5 D is bounded above by a constant r (n, kD2 ) ~ 0 , depending only on dimension , curvature and diameter. In the case when t he orbi fold has nonnegative Ricci curvature, we show that the b1 (0) is bounded above by the dimension dim 0 , a...

We define the Dirichlet to Neumann operator on exterior differential forms for a compact Riemannian manifold with boundary and prove that the real additive cohomology structure of the manifold is determined by the DN operator. In particular, an explicit formula is obtained which expresses Betti numbers of the manifold through the DN operator. We express also the Hilbert transform through the DN...

In this paper we introduce p−Ferrer diagram, note that 1− Ferrer diagram are the usual Ferrer diagrams or Ferrer board, and corresponds to planar partitions. To any p−Ferrer diagram we associate a p−Ferrer ideal. We prove that p−Ferrer ideal have Castelnuovo mumford regularity p + 1. We also study Betti numbers , minimal resolutions of p−Ferrer ideals. Every p−Ferrer ideal is p−joined ideals in...