$k$-theory $k$-theoryandhomology;cyclichomologyandcohomology $k$-theoryandoperatoralgebras 13f3514b0516e4016t0519k5619d5522e4658b3453c2458j42 14a2218d5019k3519l4719l5020f1046l5553d5558b3481r60 1921- abstract algebra algebraic algebraicgeometry analysisonmanifolds analyticfunctions approximationtheory arithmeticringsandotherspecialrings associativeringsandalgebras banachalgebras categorieswithstructure categorytheory;homologicalalgebra commutativerings commutativeringsandalgebras computersoftware congresses connectionswithlogicandautomata contactgeometry cyclic dataprocessing deformationquantization differentialgeometry dihedral equivariant$k$-theory feynmandiagrams fieldtheoryandpolynomials foundations functionalanalysis functionsofacomplexvariable functionsofcomplexvariables general generalized geometry globalanalysis globalanalysis(mathematics) globaldifferentialgeometry grouprings groupsandalgebrasinquantumtheory grouptheoryandgeneralizations higheralgebraic$k$-theory homologicalmethods hopfalgebras hopfalgebrasandtheirapplications indextheory infinite-dimensionalmanifolds instructionalexposition(textbooks integrals kasparovtheory($kk$-theory) liegroups localtheory logic mathematicallogicandfoundations mathematicalsoftware mathematics modules(algebra) noncommutativealgebraicgeometry noncommutativealgebras noncommutativedynamicalsystems noncommutativegeometry noncommutativegeometry(àlaconnes) noncommutativeglobalanalysis noncommutativeresidues operads operatortheory otherdecisionproblems partialdifferentialequationsonmanifolds;differentialoperators perturbation(quantumdynamics) pierre prüferrings quantumgroupsandrelatedtopics quantumtheory rigidityresults rings(algebra) samuel selfadjointoperatoralgebras($c^*$-algebras semisimpleliegroupsandtheirrepresentations singularities specialaspectsofinfiniteorfinitegroups starproducts symbolicandmathematical symplecticgeometry systemanalysis topological$k$-theory topologicalgroups tutorialpapers twisted$k$-theory;differential$k$-theory vonneumann($w^*$-)algebras wittvectorsandrelatedrings wordproblems