On Betti numbers of complement of hyperplanes
نویسندگان
چکیده
منابع مشابه
Betti 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 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 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 کاملOn the Betti Numbers of Chessboard Complexes
In this paper we study the Betti numbers of a type of simplicial complex known as a chessboard complex. We obtain a formula for their Betti numbers as a sum of terms involving partitions. This formula allows us to determine which is the first nonvanishing Betti number (aside from the 0-th Betti number). We can therefore settle certain cases of a conjecture of Björner, Lovász, Vrećica, and Z̆ival...
متن کاملOn the Betti Numbers of Sign Conditions
Let R be a real closed field and let Q and P be finite subsets of R[X1, . . . , Xk] such that the set P has s elements, the algebraic set Z defined by ∧ Q∈Q Q = 0 has dimension k ′ and the elements of Q and P have degree at most d. For each 0 ≤ i ≤ k′, we denote the sum of the i-th Betti numbers over the realizations of all sign conditions of P on Z by bi(P,Q). We prove that
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: Publications of the Research Institute for Mathematical Sciences
سال: 1981
ISSN: 0034-5318
DOI: 10.2977/prims/1195185267