Directed Algebraic Topology and Concurrency

“The book under review introduces a more recently developed true-concurrency model, which applies concepts and methods from algebraic topology. … I applaud the authors for having delivered what I believe is the first book in a very promising field. I highly recommend this book to mathematicians specializing in topology and seeking a challenging new application, and to those concurrency theorists who have a firm background in category theory.” (Gerald Lüttgen, Mathematical Reviews, February, 2017)“The book contains a large number of illustrative examples along with many diagrams that serve to illustrate the ideas and make the book quite easy to follow. Indeed the diagrams are an essential guide to the geometrical ideas on which the book is based. … The book can be recommended to both mathematicians and computer scientists as presentingan introduction to an area where further collaboration could be fruitful.” (J. P. E. Hodgson, Computing Reviews, computingreviews.com, July, 2016)

• 1 Introduction.- 2 A toy language for concurrency.- 3 Truly concurrent models of programs with resources.- 4 Directed topological models of concurrency.- 5 Algorithmics on directed spaces.\\