LEADER 04612nam 22007215 450 001 9910254088603321 005 20200704181450.0 010 $a81-322-2843-X 024 7 $a10.1007/978-81-322-2843-1 035 $a(CKB)3710000000872821 035 $a(DE-He213)978-81-322-2843-1 035 $a(MiAaPQ)EBC6311759 035 $a(MiAaPQ)EBC5610514 035 $a(Au-PeEL)EBL5610514 035 $a(OCoLC)959281473 035 $a(PPN)195514149 035 $a(EXLCZ)993710000000872821 100 $a20160916d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBasic Algebraic Topology and its Applications$b[electronic resource] /$fby Mahima Ranjan Adhikari 205 $a1st ed. 2016. 210 1$aNew Delhi :$cSpringer India :$cImprint: Springer,$d2016. 215 $a1 online resource (XXIX, 615 p. 176 illus.) 311 $a81-322-2841-3 327 $aPrerequisite Concepts and Notations -- Basic Homotopy -- The Fundamental Groups.-Covering Spaces -- Fibre Bundles, Vector Bundles and K-theory -- Geometry of Simplicial Complexes and Fundamental Groups -- Higher Homotopy Groups -- Products in Higher Homotopy Groups -- CW-complexes and Homotopy -- Eilenberg-MacLane Spaces -- Homology and Cohomology Theories -- Eilenberg-Steenrod Axioms for Homology and Cohomology Theories -- Consequences of the Eilenberg-Steenrod Axioms -- Some Applications of Homology Theory -- Spectral Homology and Cohomology Theories -- Obstruction Theory -- More Relations Between Homotopy and Homology Groups -- A Brief Historical Note. 330 $aThis book provides an accessible introduction to algebraic topology, a ?eld at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book o?ers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study. 606 $aAlgebraic topology 606 $aTopological groups 606 $aLie groups 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aGroup theory 606 $aK-theory 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086 615 0$aAlgebraic topology. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aGroup theory. 615 0$aK-theory. 615 14$aAlgebraic Topology. 615 24$aTopological Groups, Lie Groups. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aGroup Theory and Generalizations. 615 24$aK-Theory. 676 $a514.2 700 $aAdhikari$b Mahima Ranjan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0957608 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254088603321 996 $aBasic Algebraic Topology and its Applications$92169024 997 $aUNINA