| Directed Algebraic Topology: Models of Non-Reversible Worlds Contributor(s): Grandis, Marco (Author) |
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ISBN: 0521760364 ISBN-13: 9780521760362 Publisher: Cambridge University Press OUR PRICE: $152.00 Product Type: Hardcover - Other Formats Published: September 2009 Annotation: The first authored book to present the mathematical foundations and applications of this exciting new field. |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General |
| Dewey: 514.2 |
| Series: New Mathematical Monographs |
| Physical Information: 1.2" H x 6.1" W x 9" (1.7 lbs) 444 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This is the first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. Its general aim can be stated as 'modelling non-reversible phenomena' and its domain should be distinguished from that of classical algebraic topology by the principle that directed spaces have privileged directions and directed paths therein need not be reversible. Its homotopical tools (corresponding in the classical case to ordinary homotopies, fundamental group and fundamental groupoid) should be similarly 'non-reversible': directed homotopies, fundamental monoid and fundamental category. Homotopy constructions occur here in a directed version, which gives rise to new 'shapes', like directed cones and directed spheres. Applications will deal with domains where privileged directions appear, including rewrite systems, traffic networks and biological systems. The most developed examples can be found in the area of concurrency. |
Contributor Bio(s): Grandis, Marco: - Marco Grandis is Professor in the Department of Mathematics at the University of Genoa, Italy. |