Locally Compact Path Spaces

Abstract It is shown that the space X [0

A Characterization of BLD-Mappings Between Metric Spaces

We prove a characterization theorem for BLD-mappings between complete locally compact path-metric spaces. As a corollary, we obtain a sharp limit theorem for BLD-mappings.Peer reviewe

On Path Integral Localization and the Laplacian

We introduce a new localization principle which is a generalized canonical transformation. It unifies BRST localization, the non-abelian localization principle and a special case of the conformal Duistermaat-Heckman integration formula of Paniak, Semenoff and Szabo. The heat kernel on compact Lie groups is localized in two ways. First using a non-abelian generalization of the derivative expansion localization of Palo and Niemi and secondly using the BRST localization principle and a configuration space path integral. In addition we present some new formulas on homogeneous spaces which might be useful in a possible localization of Selberg's trace formula on locally homogeneous spaces.Comment: 30 pages LaTeX, 1 figure; published versio

Topological Full Groups of Ample Groupoids with Applications to Graph Algebras

We study the topological full group of ample groupoids over locally compact spaces. We extend Matui's definition of the topological full group from the compact, to the locally compact case. We provide two general classes of groupoids for which the topological full group, as an abstract group, is a complete isomorphism invariant. Hereby extending Matui's Isomorphism Theorem. As an application, we study graph groupoids and their topological full groups, and obtain sharper results for this class. The machinery developed in this process is used to prove an embedding theorem for ample groupoids, akin to Kirchberg's Embedding Theorem for $C^*$-algebras. Consequences for graph $C^*$-algebras and Leavitt path algebras are also spelled out. In particular, we improve on a recent embedding theorem of Brownlowe and S{\o}rensen for Leavitt path algebras.Comment: 58 pages. V4: Deleted an obsolete reference. Updated Journal reference. Minor typographical changes. (V3: Rewritten the "Our results" and "Pr\'ecis" part of the Introduction. Added Remark 6.20 and Definition 7.8.