On covering theorems

Vanishing Theorems on Covering Manifolds

Let M be an oriented even-dimensional Riemannian manifold on which a discrete group Γ of orientation-preserving isometries acts freely, so that the quotientX = M/Γ is compact. We prove a vanishing theorem for a half-kernel of a Γ-invariant Dirac operator on a Γ-equivariant Clifford module overM , twisted by a sufficiently large power of a Γ-equivariant line bundle, whose curvature is non-degene...

Covering theorems and Lebesgue integration

Abstract. This paper shows how the Lebesgue integral can be obtained as a Riemann sum and provides an extension of the Morse Covering Theorem to open sets. Let X be a finite dimensional normed space; let μ be a Radon measure on X and let Ω ⊆ X be a μ-measurable set. For λ ≥ 1, a μ-measurable set Sλ(a) ⊆ X is a λ-Morse set with tag a ∈ Sλ(a) if there is r > 0 such that B(a, r) ⊆ Sλ(a) ⊆ B(a, λr)...

Branchpoint Covering Theorems for Confluent and Weakly Confluent Maps

A branchpoint of a compactum X is a point which is the vertex of a simple triod in X. A surjective map /: X -» Y is said to cover the branchpoints of Y if each branchpoint in Y is the image of some branchpoint in X. If every map in a class % of maps on a class of compacta & covers the branchpoints of its image, then it is said that the branchpoint covering property holds for ff on 0. According ...

Covering on a Circle

On Covering Equivalence 3

An arithmetic sequence a(n) = {a+nx : x ∈ Z} (0 6 a < n) with weight λ ∈ C is denoted by 〈λ, a, n〉. For two finite systems A = {〈λs, as, ns〉}s=1 and B = {〈μt, bt,mt〉}t=1 of such triples, if ∑ ns|x−as λs = ∑ mt|x−bt μt for all x ∈ Z then we say that A and B are covering equivalent. In this paper we characterize covering equivalence in various ways, our characterizations involve the Γ-function, t...