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
050 4 _aQA440
_b.G73 2009
082 0 4 _a514.2
_222
100 1 _aGrandis, Marco,
_eauthor.
245 1 0 _aDirected algebraic topology :
_bmodels of non-reversible worlds /
_cMarco Grandis.
264 1 _aCambridge :
_bCambridge University Press,
_c2009.
300 _a1 online resource (ix, 434 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aNew mathematical monographs ;
_v13
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.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511657474
999 _c518006
_d518004