Kengo Matsumoto – författare

He’s worried she’s unhappy in their match, but little does he know she’s just desperately trying to keep her wild passion for him in check for propriety’s sake.

He’s worried she’s unhappy in their match, but little does he know she’s just desperately trying to keep her wild passion for him in check for propriety’s sake.

A samurai is worried about the fact that his wife always seems to wear a forced smile whenever she's with him. He’s worried she’s unhappy in their match, but little does he know she’s just desperately trying to keep her wild passion for him in check for propriety’s sake.

This book presents the interplay between topological Markov shifts and Cuntz–Krieger algebras by providing notations, techniques, and ideas in detail. The main goal of this book is to provide a detailed proof of a classification theorem for continuous orbit equivalence of one-sided topological Markov shifts. The continuous orbit equivalence of one-sided topological Markov shifts is classified in terms of several different mathematical objects: the étale groupoids, the actions of the continuous full groups on the Markov shifts, the algebraic type of continuous full groups, the Cuntz–Krieger algebras, and the K-theory dates of the Cuntz–Krieger algebras. This classification result shows that topological Markov shifts have deep connections with not only operator algebras but also groupoid theory, infinite non-amenable groups, group actions, graph theory, linear algebras, K-theory, and so on. By using this classification result, the complete classification of flow equivalence in two-sided topological Markov shifts is described in terms of Cuntz–Krieger algebras. The author will also study the relationship between the topological conjugacy of topological Markov shifts and the gauge actions of Cuntz–Krieger algebras.