Related papers: Twisted Topological Graph Algebras
We study twisted derived equivalences for schemes in the setting of spectral algebraic geometry. To this end, we introduce the notion of a twisted equivalence and show that a twisted equivalence for perfect spectral algebraic stacks…
We prove that the twisted K-homology of a simply connected simple Lie group G of rank n is an exterior algebra on n-1 generators tensor a cyclic group. We give a detailed description of the order of this cyclic group in terms of the…
The Kinoshita graph is a particular embedding in the 3-sphere of a graph with three edges, two vertices and no loops. It has the remarkable property that although the removal of any edge results in an unknotted loop, the Kinoshita graph is…
These are notes on twisted K-homology theory and twisted Ext-theory from the C*-algebra viewpoint, part of a series of talks on ``C*-algebras, noncommutative geometry and K-theory'', primarily for physicists.
A graph is universally $k$-edge-weightable if for every $k$-element set $Q\subset\mathbb{R}$, it admits a proper $Q$-edge weighting. The settled 1-2-3 conjecture implies that for any arithmetic progression $\{a,b,c\}$, every nice regular…
We study conditions that ensure uniqueness theorems of Cuntz-Krieger type for relative Cuntz-Pimsner algebras $\mathcal{O}(J,X)$ associated to a $C^*$-correspondence $X$ over a $C^*$-algebra $A$. We give general sufficient conditions…
For a Koszul Artin-Schelter regular algebra (also called twisted Calabi-Yau algebra), we show that it has a "twisted" bi-symplectic structure, which may be viewed as a noncommutative and twisted analogue of the shifted symplectic structure…
We provide groupoid models for Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs. Extending the groupoid models used in the theory of graph algebras and topological dynamical systems to our setting, we prove results on…
Circulant graphs are a widely studied family of graphs whose members possess varying amounts of symmetry. Although considerable progress has been made in finding the automorphism groups of circulant graphs under certain restrictions, a…
A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis,…
This thesis captures the ongoing development of twisted cubes, which is a modification of cubes (in a topological sense) where its homotopy type theory does not require paths or higher paths to be invertible. My original motivation to…
Motivated by the theory of Cuntz-Krieger algebras we define and study $ C^\ast $-algebras associated to directed quantum graphs. For classical graphs the $ C^\ast $-algebras obtained this way can be viewed as free analogues of Cuntz-Krieger…
This is a PhD thesis in low-dimensional topology. Its main purpose is to examine so-called t\^ete-\`a-t\^ete twists. Those were defined by A'Campo and give an easy combinatorial description of certain mapping classes on surfaces with…
Extending the work of Godsil and others, we investigate the notion of the inverse of a graph (specifically, of bipartite graphs with a unique perfect matching). We provide a concise necessary and sufficient condition for the invertibility…
We show the topological Hochschild homology spectrum of a twisted group algebra $\THH(A^{\tau}[G])$ is the Thom spectrum associated to a parametrized orthogonal spectrum $E(A,G)$. We then analyze the structure of the parametrized orthogonal…
Cuntz algebras $\mathcal{O}_n$, $n>1$, are celebrated examples of a separable infinite simple C*-algebra with a number of fascinating properties. Their K-theory allows an embedding of $\mathcal O_m$ in $\mathcal O_n$ whenever $n-1$ divides…
We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…
Many previously studied path algebras or self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid…
Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…
We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C*-correspondences and Cuntz-Pimsner algebras. We show that the C*-algebra…