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001 978-3-540-71962-5
003 DE-He213
005 20161121231213.0
007 cr nn 008mamaa
008 100301s2008 gw | s |||| 0|eng d
020 _a9783540719625
_9978-3-540-71962-5
024 7 _a10.1007/978-3-540-71962-5
_2doi
050 4 _aQA612-612.8
072 7 _aPBPD
_2bicssc
072 7 _aMAT038000
_2bisacsh
082 0 4 _a514.2
_223
100 1 _aKozlov, Dmitry.
_eauthor.
245 1 0 _aCombinatorial Algebraic Topology
_h[electronic resource] /
_cby Dmitry Kozlov.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2008.
300 _aXX, 390 p. 115 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAlgorithms and Computation in Mathematics,
_x1431-1550 ;
_v21
505 0 _aConcepts of Algebraic Topology -- Overture -- Cell Complexes -- Homology Groups -- Concepts of Category Theory -- Exact Sequences -- Homotopy -- Cofibrations -- Principal ?-Bundles and Stiefel—Whitney Characteristic Classes -- Methods of Combinatorial Algebraic Topology -- Combinatorial Complexes Melange -- Acyclic Categories -- Discrete Morse Theory -- Lexicographic Shellability -- Evasiveness and Closure Operators -- Colimits and Quotients -- Homotopy Colimits -- Spectral Sequences -- Complexes of Graph Homomorphisms -- Chromatic Numbers and the Kneser Conjecture -- Structural Theory of Morphism Complexes -- Using Characteristic Classes to Design Tests for Chromatic Numbers of Graphs -- Applications of Spectral Sequences to Hom Complexes.
520 _aCombinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field.
650 0 _aMathematics.
650 0 _aAlgebraic topology.
650 0 _aCombinatorics.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Topology.
650 2 4 _aCombinatorics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540719618
830 0 _aAlgorithms and Computation in Mathematics,
_x1431-1550 ;
_v21
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-540-71962-5
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c510089
_d510089