LEADER 02817nam 22004335a 450 001 9910151928803321 005 20110815234510.0 010 $a3-03719-583-5 024 70$a10.4171/083 035 $a(CKB)3710000000953870 035 $a(CH-001817-3)130-110815 035 $a(PPN)178155942 035 $a(EXLCZ)993710000000953870 100 $a20110815j20110811 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNonabelian Algebraic Topology$b[electronic resource] $eFiltered Spaces, Crossed Complexes, Cubical Homotopy Groupoids /$fRonald Brown, Philip J. Higgins, Rafael Sivera 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2011 215 $a1 online resource (703 pages) 225 0 $aEMS Tracts in Mathematics (ETM)$v15 330 $aThe main theme of this book is that the use of filtered spaces rather than just topological spaces allows the development of basic algebraic topology in terms of higher homotopy groupoids; these algebraic structures better reflect the geometry of subdivision and composition than those commonly in use. Exploration of these uses of higher dimensional versions of groupoids has been largely the work of the first two authors since the mid 1960s. The structure of the book is intended to make it useful to a wide class of students and researchers for learning and evaluating these methods, primarily in algebraic topology but also in higher category theory and its applications in analogous areas of mathematics, physics and computer science. Part I explains the intuitions and theory in dimensions 1 and 2, with many figures and diagrams, and a detailed account of the theory of crossed modules. Part II develops the applications of crossed complexes. The engine driving these applications is the work of Part III on cubical ?-groupoids, their relations to crossed complexes, and their homotopically defined examples for filtered spaces. Part III also includes a chapter suggesting further directions and problems, and three appendices give accounts of some relevant aspects of category theory. Endnotes for each chapter give further history and references. 606 $aAlgebraic topology$2bicssc 606 $aAlgebraic topology$2msc 606 $aCategory theory; homological algebra$2msc 615 07$aAlgebraic topology 615 07$aAlgebraic topology 615 07$aCategory theory; homological algebra 686 $a55-xx$a18-xx$2msc 700 $aBrown$b Ronald$01026750 702 $aHiggins$b Philip J. 702 $aSivera$b Rafael 801 0$bch0018173 906 $aBOOK 912 $a9910151928803321 996 $aNonabelian Algebraic Topology$92565660 997 $aUNINA