- Directed algebraic topology
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In mathematics, directed algebraic topology is a form of algebraic topology that studies topological spaces equipped with a family of directed paths, closed under some operations. The term d-space is applied to these spaces. Directed algebraic topology is a subject that emerged in the 1990s. 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 group and fundamental n-groupoids, are similarly 'non-reversible': directed homotopies, fundamental monoids and fundamental ncategories. 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.[1]
References
- ^ Directed Algebraic Topology: Models of Non-Reversible Worlds, Marco Grandis, Cambridge University Press, ISBN 9780521760362
Further reading
- Directed homotopy theory, I. The fundamental category, Marco Grandis
- Directed homotopy theory, II. Homotopy Constructs, Marco Grandis, Theory and Applications of Categories, Vol. 10, No. 14, 2002, pp. 369–391
- A Few Points On Directed Algebraic Topology, Marco Grandis
- Directed combinatorial homology and noncommutative tori, Marco Grandis, Math. Proc. Cambridge Philos. Soc. 138 (2005), 233-262
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