A coarse embedding theorem for homological filling functions

Homological and Homotopical Higher-order Filling Functions

We construct groups in which FV (n) ≁ δ(n). This construction also leads to groups Gk, k ≥ 3 for which δ (n) is not subrecursive. The Dehn function of a group provides a measure of the complexity of the group’s word problem by measuring the difficulty of filling loops in a corresponding complex. A natural generalization is to consider the difficulty of filling higher-dimensional manifolds or cy...

Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

An Operator Embedding Theorem for Complexity Classes of Recursive Functions

A Homological Theory of Functions

In computational complexity, a complexity class is given by a set of problems or functions, and a basic challenge is to show separations of complexity classes A 6= B especially when A is known to be a subset of B. In this paper we introduce a homological theory of functions that can be used to establish complexity separations, while also providing other interesting consequences. We propose to a...

A localization theorem in homological algebra

Introduction. In (l), J. F. Adams showed that for p odd, the Adams 2? 2-term for a sphere, Ext5*(F p , F p), is zero for s < t < (2p-l)s-l, while Ext^ s (Fj,, F p) is the one-dimensional vector space generated by ql, where g