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.
General
Imprint: |
Cambridge UniversityPress
|
Country of origin: |
United Kingdom |
Series: |
New Mathematical Monographs |
Release date: |
September 2009 |
First published: |
October 2009 |
Authors: |
Marco Grandis
|
Dimensions: |
234 x 160 x 30mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
444 |
ISBN-13: |
978-0-521-76036-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Topology >
Analytic topology
|
LSN: |
0-521-76036-4 |
Barcode: |
9780521760362 |
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