Directed Algebraic Topology and Concurrency

Heath provided us with a fantastic book on algebraic topology and concurrency.

It’s authored by¬†Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, and Martin Raussen.

Here’s the “Plan of the Book”:

We begin by introducing a toy programming language, provide its interleaving semantics, and describe the properties of programs we are interested in (Chap. 2). We then add resources, such as mutexes in the language, and provide truly concurrent semantics for programs; such semantics at first involve asynchronous graphs, and later generalize to precubical sets (Chap. 3). The notion of a directed topological space is introduced and used to provide new semantics, and we discuss a suitable notion of homotopy between paths in the resulting models (Chap. 4). Algorithms based on the geometric semantics are then described for computing: cubical regions, deadlocks, and factorizing processes (Chap. 5). The two next chapters discuss more advanced topics: categories of components (Chap. 6) and paths spaces (Chap. 7). Finally, we conclude by hinting at topics not covered in the book and future developments (Chap. 8).

And here’s the cover image:

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