Directed Algebraic Topology

High Quality Content by WIKIPEDIA articles! In mathematics, directed algebraic topology is a form of algebraic topology that studies topological spaces equipped with a direction. The generic term directed spaces is applied to such spaces. Directed algebraic topology is a subject that emerged in the 1990s to meet the need for models of Concurrency (computer science). Its domain is distinguished from classical algebraic topology by the principle that directed spaces have privileged directions and that the directed paths therein need not be reversible. Its homotopical tools, corresponding to ordinary homotopies, fundamental groups and fundamental n-groupoids, are similarly \'non-reversible\': directed homotopies, fundamental monoids and fundamental n-categories. Its applications deal with domains where privileged directions appear, like concurrent processes, traffic networks, spacetime models, noncommutative geometry, rewriting systems and the modelling of biological systems. Dannoe izdanie predstavlyaet soboj kompilyatsiyu svedenij, nahodyaschihsya v svobodnom dostupe v srede Internet v tselom, i v informatsionnom setevom resurse "Vikipediya" v chastnosti. Sobrannaya po chastotnym zaprosam ukazannoj tematiki, dannaya kompilyatsiya postroena po printsipu podbora blizkih informatsionnyh ssylok, ne imeet samostoyatelnogo syuzheta, ne soderzhit nikakih analiticheskih materialov, vyvodov, otsenok moralnogo, eticheskogo, politicheskogo, religioznogo i mirovozzrencheskogo haraktera v otnoshenii glavnoj tematiki, predstavlyaya soboj isklyuchitelno faktologicheskij material. This book was created using print-on-demand technology.