| 000 | 02570nam a22003498i 4500 | ||
|---|---|---|---|
| 001 | CR9780511657474 | ||
| 003 | UkCbUP | ||
| 005 | 20200124160235.0 | ||
| 006 | m|||||o||d|||||||| | ||
| 007 | cr|||||||||||| | ||
| 008 | 091208s2009||||enk o ||1 0|eng|d | ||
| 020 | _a9780511657474 (ebook) | ||
| 020 | _z9780521760362 (hardback) | ||
| 040 |
_aUkCbUP _beng _erda _cUkCbUP |
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| 050 | 4 |
_aQA440 _b.G73 2009 |
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| 082 | 0 | 4 |
_a514.2 _222 |
| 100 | 1 |
_aGrandis, Marco, _eauthor. |
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| 245 | 1 | 0 |
_aDirected algebraic topology : _bmodels of non-reversible worlds / _cMarco Grandis. |
| 264 | 1 |
_aCambridge : _bCambridge University Press, _c2009. |
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| 300 |
_a1 online resource (ix, 434 pages) : _bdigital, PDF file(s). |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 490 | 1 |
_aNew mathematical monographs ; _v13 |
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| 500 | _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). | ||
| 505 | 0 | _aFirst-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. | |
| 520 | _aThis 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. | ||
| 650 | 0 | _aAlgebraic topology. | |
| 776 | 0 | 8 |
_iPrint version: _z9780521760362 |
| 830 | 0 |
_aNew mathematical monographs ; _v13. |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1017/CBO9780511657474 |
| 999 |
_c518006 _d518004 |
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