منابع مشابه
-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...
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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 ...
متن کاملBetti Numbers and Injectivity Radii
The theme of this paper is the connection between topological properties of a closed orientable hyperbolic 3-manifold M and the maximal injectivity radius of M . In [4] we showed that if the first Betti number of M is at least 3 then the maximal injectivity radius of M is at least log 3. By contrast, the best known lower bound for the maximal injectivity radius of M with no topological restrict...
متن کاملBetti numbers are testable ∗
We prove that the Betti numbers of simplicial complexes of bounded vertex degrees are testable in constant time.
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ژورنال
عنوان ژورنال: Mathematical Notes
سال: 2014
ISSN: 0001-4346,1573-8876
DOI: 10.1134/s0001434614050307