Cohomology of maximal ideal spaces

Uniform Approximation and Maximal Ideal Spaces

Let X be a compact set in the z-plane. We are interested in two function spaces associated with X: C(X) — space of all continuous complex-valued functions on X. P(X) =space of all uniform limits of polynomials on X. Thus a function ƒ on X lies in P{X) if there exists a sequence {Pn} of polynomials converging to ƒ uniformly on X. Clearly P(X) is part of C(X). QUESTION I. When is P(X) = C(X)t i.e...

Certain subalgebras of Lipschitz algebras of infinitely differentiable functions and their maximal ideal spaces

We study an interesting class of Banach function algebras of innitely dierentiable functions onperfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, calledLipschitz algebras of innitely dierentiable functions and denoted by Lip(X;M; ), where X is aperfect, compact plane set, M = fMng1n=0 is a sequence of positive numbers such that M0 = 1 and(m+n)!Mm+n ( m!Mm)...

Twisted cohomology of configuration spaces of the plane and spaces of maximal tori via point-counting

We consider two families of algebraic varieties Yn indexed by natural numbers n: the configuration space of unordered n-tuples of distinct points on C, and the space of unordered n-tuples of linearly independent lines in C. Let Wn be any sequence of virtual Sn-representations given by a character polynomial, we compute H(Yn;Wn) for all i and all n in terms of double generating functions. One co...

Cohomology of Algebraic Spaces

Cohomology of Braid Spaces

where C+F(R9 p) denotes the singular chains of F(R , p), and Zp{q) denotes the Ip-module Zp with 2P-action a • x = ( l) x for xeZp and a e Zp ( ( 1) S(<T) is the sign of a). Since the Enaction on F(R, p) is proper, we may identify H*(HomEp(C^F(« , p) ; Zp(2g))) with H*(B(R ,p); Zp) [5]. By abuse of notation we denote H*(Hom2 ( Q F ^ p ) ; Zp(g))) by H*(B(R\p);Zp(q)). The interest in H*(B(R, p) ...