Characterizing certain semidualizing complexes via their Betti and Bass numbers
نویسندگان
چکیده
Two distinguished types of semidualizing complexes are the shifts underlying rings and dualizing complexes. Let C be a complex for an analytically irreducible local ring R set n:=supC d:=dimRC. We show that is quasi-isomorphic to shift if only nth Betti number one. Also, we dth Bass
منابع مشابه
Random 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 کاملBounding Helly Numbers via Betti Numbers
We show that very weak topological assumptions are enough to ensure the existence of a Hellytype theorem. More precisely, we show that for any non-negative integers b and d there exists an integer h(b, d) such that the following holds. If F is a finite family of subsets of R such that β̃i ( ⋂G) ≤ b for any G ( F and every 0 ≤ i ≤ dd/2e−1 then F has Helly number at most h(b, d). Here β̃i denotes t...
متن کاملExtremal Betti Numbers of Rips Complexes
Upper bounds on the topological Betti numbers of Vietoris-Rips complexes are established, and examples of such complexes with high Betti
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 کاملPersistent Betti numbers of random Čech complexes
We study the persistent homology of random Čech complexes. Generalizing a method of Penrose for studying random geometric graphs, we first describe an appropriate theoretical framework in which we can state and address our main questions. Then we define the kth persistent Betti number of a random Čech complex and determine its asymptotic order in the subcritical regime. This extends a result of...
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: Communications in Algebra
سال: 2022
ISSN: ['1532-4125', '0092-7872']
DOI: https://doi.org/10.1080/00927872.2022.2032727