منابع مشابه
Betti Numbers of Graded Modules and Cohomology of Vector Bundles
In a remarkable paper Mats Boij and Jonas Söderberg [2006] conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring is a positive linear combination of Betti tables of modules with pure resolutions. We prove a strengthened form of their Conjectures. Applications include a proof of the Multiplicity Conjecture of Huneke and Srinivasan and a proof of the convexity of a fa...
متن کامل-betti Numbers
The Atiyah conjecture predicts that the L-Betti numbers of a finite CW -complex with torsion-free fundamental group are integers. We show that the Atiyah conjecture holds (with an additional technical condition) for direct and inverse limits of groups for which it is true. As a corollary it holds for residually torsion-free solvable groups, e.g. for pure braid groups or for positive 1-relator g...
متن کاملRandom Complexes and l 2 - Betti Numbers
Uniform spanning trees on finite graphs and their analogues on infinite graphs are a well-studied area. On a Cayley graph of a group, we show that they are related to the first l-Betti number of the group. Our main aim, however, is to present the basic elements of a higher-dimensional analogue on finite and infinite CW-complexes, which relate to the higher l-Betti numbers. One consequence is a ...
متن کاملOn 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...
متن کاملBetti numbers of subgraphs
Let G be a simple graph on n vertices. LetH be either the complete graph Km or the complete bipartite graph Kr,s on a subset of the vertices in G. We show that G contains H as a subgraph if and only if βi,α(H) ≤ βi,α(G) for all i ≥ 0 and α ∈ Z. In fact, it suffices to consider only the first syzygy module. In particular, we prove that β1,α(H) ≤ β1,α(G) for all α ∈ Z if and only if G contains a ...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2002
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2002.6.541