共查询到20条相似文献,搜索用时 0 毫秒
1.
Jonathan Block Varghese Mathai Shmuel Weinberger 《Proceedings of the American Mathematical Society》1997,125(12):3757-3762
We give short proofs of the Gromov-Shubin theorem on the homotopy invariance of the Novikov-Shubin invariants and of the Dodziuk theorem on the homotopy invariance of the Betti numbers of the universal covering of a closed manifold in this paper. We show that the homotopy invariance of these invariants is no more difficult to prove than the homotopy invariance of ordinary homology theory.
2.
Marc Chardin Vesselin Gasharov Irena Peeva 《Proceedings of the American Mathematical Society》2002,130(7):1877-1880
We provide a short proof that the lexicographic ideal has the greatest Betti numbers among all graded ideals with a fixed Hilbert function.
3.
N. Ozawa 《Geometric And Functional Analysis》2003,13(1):216-222
We prove that AF-embeddability is a homotopy invariant in the class
of separable exact C
*-algebras. This work was inspired by Spielberg's
work on homotopy invariance of AF-embeddability and Dadarlat's
serial works on AF-embeddability of residually finite dimensional C
*-algebras.
Submitted: February 2002. 相似文献
4.
We discuss growth rates of Betti numbers in a family of coverings of a compact cell complex X, when the corresponding L2 Betti number of X is zero. We show that the Betti numbers are bounded by a function, sub-linear in the order of the covering. If the appropriate Novikov-Shubin invariant of X is positive, the rate bounds are improved. For well behaved families (such as congruence covers of symmetric spaces), if the L2 spectrum of X? has a gap at zero then the growth rate is bounded by the order of the covering raised to a power less than one. 相似文献
5.
6.
S. E. Stepanov 《Mathematical Notes》2014,95(5-6):856-864
The Tachibana numbers t r (M), the Killing numbers k r (M), and the planarity numbers p r (M) are considered as the dimensions of the vector spaces of, respectively, all, coclosed, and closed conformal Killing r-forms with 1 ≤ r ≤ n ? 1 “globally” defined on a compact Riemannian n-manifold (M,g), n >- 2. Their relationship with the Betti numbers b r (M) is investigated. In particular, it is proved that if b r (M) = 0, then the corresponding Tachibana number has the form t r (M) = k r (M) + p r (M) for t r (M) > k r (M) > 0. In the special case where b 1(M) = 0 and t 1(M) > k 1(M) > 0, the manifold (M,g) is conformally diffeomorphic to the Euclidean sphere. 相似文献
7.
Rosa M. Mir-Roig 《Journal of Algebra》2007,318(2):653-668
Let R=k[x1,…,xn] be a polynomial ring and let IR be a graded ideal. In [T. Römer, Betti numbers and shifts in minimal graded free resolutions, arXiv: AC/070119], Römer asked whether under the Cohen–Macaulay assumption the ith Betti number βi(R/I) can be bounded above by a function of the maximal shifts in the minimal graded free R-resolution of R/I as well as bounded below by a function of the minimal shifts. The goal of this paper is to establish such bounds for graded Cohen–Macaulay algebras k[x1,…,xn]/I when I is a standard determinantal ideal of arbitrary codimension. We also discuss other examples as well as when these bounds are sharp. 相似文献
8.
It is shown that, for certain congruence families of Galois coverings of a manifold, the individual Betti numbers are polynomial periodic functions of the level. Similar results are proved for the dimensions of other spaces of automorphic forms. 相似文献
9.
Betti numbers of configuration spaces of mechanical linkages (known also as polygon spaces) depend on a large number of parameters – the lengths of the bars of the linkage. Motivated by applications in topological robotics, statistical shape theory and molecular biology, we view these lengths as random variables and study asymptotic values of the average Betti numbers as the number of links n tends to infinity. We establish a surprising fact that for a reasonably ample class of sequences of probability measures the asymptotic values of the average Betti numbers are independent of the choice of the measure. The main results of the paper apply to planar linkages as well as for linkages in R 3. We also prove results about higher moments of Betti numbers. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
Irena Peeva 《Proceedings of the American Mathematical Society》2004,132(12):3503-3507
Let be a homogeneous ideal in a polynomial ring over a field. By Macaulay's Theorem, there exists a lexicographic ideal with the same Hilbert function as . We prove that the graded Betti numbers of are obtained from those of by a sequence of consecutive cancellations.
11.
Shûkichi Tanno 《Mathematische Annalen》1970,190(2):135-148
12.
We prove the following general homotopy invariance theorem for coherent Witt groups: Let be a flat morphism of separated Gorenstein schemes of finite Krull dimension with affine fibers,i.e. π−1(y) is an affine space over the residue field k(y) for all yY, then the induced homomorphism of coherent Witt groups is an isomorphism. As an application we calculate the (classical) Witt group of the affine hyperbolic sphere over a regular
local ring.
Received: 22 August 2001; in final form: 22 June 2002 /
Published online: 1 April 2003 相似文献
13.
Giuseppe Valla 《Proceedings of the American Mathematical Society》2005,133(1):57-63
In this paper we compute the graded Betti numbers of certain monomial ideals that are not stable. As a consequence we prove a conjecture, stated by G. Fatabbi, on the graded Betti numbers of two general fat points in
14.
Giancarlo Rinaldo 《Archiv der Mathematik》2008,91(5):416-426
We compute the Betti numbers of the resolution of a special class of square-free monomial ideals, the ideals of mixed products.
Moreover when these ideals are Cohen-Macaulay we calculate their type.
Received: 9 March 2008 相似文献
15.
We prove that multigraded Betti numbers of a simplicial forest are always either 0 or 1. Moreover a nonzero multidegree appears exactly in one homological degree in the resolution. Our work generalizes work of Bouchat [2] on edge ideals of graph trees. 相似文献
16.
Archiv der Mathematik - Let A be an algebra over a field F of characteristic zero. For every $$n\ge 1$$ , let $$\delta _n(A)$$ be the number of linearly independent multilinear proper central... 相似文献
17.
The possible extremal Betti numbers of graded ideals in the polynomial ring K[x1,…,xn] in n variables with coefficients in a field K are studied, completing our results in [7]. In case char(K) = 0 we determine, given any integers r < n, the conditions under which there exists a graded ideal I ? K[x1,…, xn] with extremal Betti numbers $\beta_{k_{i}k_{i}+\ell_{i}}\ {\rm for}\ i=1,\cdots,r$ . We also treat a similar problem for squarefree lexsegment ideals. 相似文献
18.
A multicomplexM is a collection of monomials closed under divisibility. For suchM we construct a cell complex M whosei-dimensional cells are in bijection with thef
i
monomials ofM of degreei+1. The bijection is such that the inclusion relation of cells corresponds to divisibility of monomials. We then study relations between the numbersf
i
and the Betti numbers of M. For squarefree monomials the construction specializes to the standard geometric realization of a simplicial complex.This work was supported by the Mittag-Leffler Institute during the Combinatorial Year program 1991–92. The second author also acknowledges support from the Serbian Science Foundation, Grant No. 0401D. 相似文献
19.
A vanishing theorem and constraints are given for the Betti numbers of compact 3-Sasakian manifolds. 相似文献
20.
Anna Lorenzini 《Journal of Pure and Applied Algebra》1989,60(3):273-288
In this paper we study the graded minimal free resolution of the ideal, I, of any arithmetically Cohen-Macaulay projective variety. First we determine the range of the shifts (twisting numbers) that can possibly occur in the resolution, in terms of the Hilbert function of I. Then we find conditions under which some of the twisting numbers do not occur. Finally, in some ‘good’ cases, all the Betti numbers are (recursively) computed, in terms of the Hilbert function of I or that of ExtnR(R/I,R), where R is a polynomial ring over a field and n is the height of I in R. 相似文献