LEADER 04343nam 22004695a 450 001 9910151933703321 005 20091109150325.0 010 $a3-03719-560-6 024 70$a10.4171/060 035 $a(CKB)3710000000953838 035 $a(CH-001817-3)89-091109 035 $a(PPN)178155543 035 $a(EXLCZ)993710000000953838 100 $a20091109j20081006 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aK-Theory and Noncommutative Geometry$b[electronic resource] /$fGuillermo Cortin?as, Joachim Cuntz, Max Karoubi, Ryszard Nest, Charles A. Weibel 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2008 215 $a1 online resource (454 pages) 225 0 $aEMS Series of Congress Reports (ECR) ;$x2523-515X 327 $tCategorical aspects of bivariant K-theory /$rRalf Meyer --$tInheritance of isomorphism conjectures under colimits /$rArthur Bartels, Siegfried Echterhoff, Wolfgang Lu?ck --$tCoarse and equivariant co-assembly maps /$rHeath Emerson, Ralf Meyer --$tOn K1 of a Waldhausen category /$rFernando Muro, Andrew Tonks --$tTwisted K-theory - old and new /$rMax Karoubi --$tEquivariant cyclic homology for quantum groups /$rChristian Voigt --$tA Schwartz type algebra for the tangent groupoid /$rPaulo Carrillo Rouse --$tC*-algebras associated with the ax?+?b-semigroup over ? /$rJoachim Cuntz --$tOn a class of Hilbert C*-manifolds /$rWend Werner --$tDuality for topological abelian group stacks and T-duality /$rUlrich Bunke, Thomas Schick, Markus Spitzweck, Andreas Thom --$tDeformations of gerbes on smooth manifolds /$rPaul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris Tsygan --$tTorsion classes of finite type and spectra /$rGrigory Garkusha, Mike Prest --$tParshin's conjecture revisited /$rThomas Geisser --$tAxioms for the norm residue isomorphism /$rCharles A. Weibel. 330 $aSince its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus K-theory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory. To study noncommutative geometric problems one considers invariants of the relevant noncommutative algebras. These invariants include algebraic and topological K-theory, and also cyclic homology, discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative version of de Rham cohomology and as an additive version of K-theory. There are primary and secondary Chern characters which pass from K-theory to cyclic homology. These characters are relevant both to noncommutative and commutative problems, and have applications ranging from index theorems to the detection of singularities of commutative algebraic varieties. The contributions to this volume represent this range of connections between K-theory, noncommmutative geometry, and other branches of mathematics. 606 $aAlgebraic geometry$2bicssc 606 $a$K$-theory$2msc 606 $aGlobal analysis, analysis on manifolds$2msc 615 07$aAlgebraic geometry 615 07$a$K$-theory 615 07$aGlobal analysis, analysis on manifolds 686 $a19-xx$a58-xx$2msc 702 $aCortin?as$b Guillermo 702 $aCuntz$b Joachim 702 $aKaroubi$b Max 702 $aNest$b Ryszard 702 $aWeibel$b Charles A. 801 0$bch0018173 906 $aBOOK 912 $a9910151933703321 996 $aK-Theory and Noncommutative Geometry$92565019 997 $aUNINA