Directed algebraic topology: models of non-reversible worlds
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 distinguishe...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2009
|
| Schriftenreihe: | New mathematical monographs
13 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (ix, 434 pages) |
| ISBN: | 9780511657474 |
| DOI: | 10.1017/CBO9780511657474 |
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| 245 | 1 | 0 | |a Directed algebraic topology |b models of non-reversible worlds |c Marco Grandis |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a First-order directed homotopy and homology -- Directed structures and first-order homotopy properties -- Directed homology and non-commutative geometry -- Modelling the fundamental category -- Higher directed homotopy theory -- Settings for higher order homotopy -- Categories of functors and algebras, relative settings -- Elements of weighted algebraic topology | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Grandis, Marco |
| author_facet | Grandis, Marco |
| author_role | aut |
| author_sort | Grandis, Marco |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | BV043941834 |
| classification_rvk | SK 300 SK 340 |
| collection | ZDB-20-CBO |
| contents | First-order directed homotopy and homology -- Directed structures and first-order homotopy properties -- Directed homology and non-commutative geometry -- Modelling the fundamental category -- Higher directed homotopy theory -- Settings for higher order homotopy -- Categories of functors and algebras, relative settings -- Elements of weighted algebraic topology |
| ctrlnum | (ZDB-20-CBO)CR9780511657474 (OCoLC)967601057 (DE-599)BVBBV043941834 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511657474 |
| format | Electronic eBook |
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| id | DE-604.BV043941834 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511657474 |
| language | English |
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| publishDate | 2009 |
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| spelling | Grandis, Marco Verfasser aut Directed algebraic topology models of non-reversible worlds Marco Grandis Cambridge Cambridge University Press 2009 1 online resource (ix, 434 pages) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 13 Title from publisher's bibliographic system (viewed on 05 Oct 2015) First-order directed homotopy and homology -- Directed structures and first-order homotopy properties -- Directed homology and non-commutative geometry -- Modelling the fundamental category -- Higher directed homotopy theory -- Settings for higher order homotopy -- Categories of functors and algebras, relative settings -- Elements of weighted algebraic topology 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 Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-76036-2 https://doi.org/10.1017/CBO9780511657474 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Grandis, Marco Directed algebraic topology models of non-reversible worlds First-order directed homotopy and homology -- Directed structures and first-order homotopy properties -- Directed homology and non-commutative geometry -- Modelling the fundamental category -- Higher directed homotopy theory -- Settings for higher order homotopy -- Categories of functors and algebras, relative settings -- Elements of weighted algebraic topology Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 |
| title | Directed algebraic topology models of non-reversible worlds |
| title_auth | Directed algebraic topology models of non-reversible worlds |
| title_exact_search | Directed algebraic topology models of non-reversible worlds |
| title_full | Directed algebraic topology models of non-reversible worlds Marco Grandis |
| title_fullStr | Directed algebraic topology models of non-reversible worlds Marco Grandis |
| title_full_unstemmed | Directed algebraic topology models of non-reversible worlds Marco Grandis |
| title_short | Directed algebraic topology |
| title_sort | directed algebraic topology models of non reversible worlds |
| title_sub | models of non-reversible worlds |
| topic | Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraic topology Algebraische Topologie |
| url | https://doi.org/10.1017/CBO9780511657474 |
| work_keys_str_mv | AT grandismarco directedalgebraictopologymodelsofnonreversibleworlds |