ENGLISH

Directed algebraic topology: Models of non-reversible worlds

By Marco Grandis

Book information

Publisher
Cambridge University Press
Year
2009
ISBN
0521760364, 9780521760362
LCC
QA612 .G68 2009
Open Library ID
OL24385409M
Language
english
Format
PDF
Filesize
2 MB (2052978 bytes)
Series
New Mathematical Monographs
Edition
1
Pages
446\446
Library
Kolxo3
Scanned
yes
Time added
2010-07-29 05:14:56

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.

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