The definitive reference for this field is the book by Maurice Herlihy, Dmitry Kozlov, and Sergio Rajsbaum (2013). Distributed Computing Through Combinatorial Topology
Protocols then act like maps from an input complex (possible initial configurations) to an output complex (possible decision values), but with strong locality constraints: a process can only base its decision on information it can causally learn. These local constraints translate into combinatorial continuity properties of the map — analogous to continuity in topology: nearby input configurations (indistinguishable to some process) must map to nearby outputs (the same decision for that process). distributed computing through combinatorial topology pdf