Rational Betti numbers of configuration spaces
نویسندگان
چکیده
منابع مشابه
The First Betti Numbers of Certain Locally Trivial Fibre Spaces
The purpose of this department is to provide early announcement of significant new results, with some indications of proof. Although ordinarily a research announcement should be a brief summary of a paper to be published in full elsewhere, papers giving complete proofs of results of exceptional interest are also solicited. Manuscripts more than eight typewritten double spaced pages long will no...
متن کاملSome remarks on Betti numbers of random polygon spaces
Polygon spaces such as M = {(u1, . . . , un) ∈ S1 × . . . S1,∑ni=1 liui = 0}/SO(2), or the three-dimensional analogs N play an important rôle in geometry and topology, and are also of interest in robotics where the li model the lengths of robot arms. When n is large, one can assume that each li is a positive real valued random variable, leading to a randommanifold. The complexity of such manifo...
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 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 ...
متن کاملBetti Numbers of Graphs
This paper describes an application of research that sits at the intersection of commutative algebra and combinatorics: Betti numbers of graphs. In particular, we describe a correspondence between simple undirected graphs and a class of ideals in a polynomial ring. We then briefly introduce some of the algebraic invariants that can be associated to the ideal and the relation of these invariants...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2000
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(98)00148-5