LEADER 03089nam 2200565 450 001 9910539691103321 005 20200923020339.0 010 $a3-11-054348-6 024 7 $a10.1515/9783110545258 035 $a(CKB)4100000001044486 035 $a(MiAaPQ)EBC5150943 035 $a(DE-B1597)480963 035 $a(OCoLC)1013826258 035 $a(DE-B1597)9783110545258 035 $a(Au-PeEL)EBL5150943 035 $a(CaPaEBR)ebr11471630 035 $a(EXLCZ)994100000001044486 100 $a20171220h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aNoncommutative geometry $ea functorial approach /$fIgor V. Nikolaev 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (266 pages) $cillustrations 225 1 $aDe Gruyter Studies in Mathematics,$x0179-0986 ;$vVolume 66 311 $a3-11-054317-6 311 $a3-11-054525-X 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tPreface -- $tContents -- $tIntroduction -- $tPart I: Basics -- $t1. Model examples -- $t2. Categories and functors -- $t3. C?-algebras -- $tPart II: Noncommutative invariants -- $t4. Topology -- $t5. Algebraic geometry -- $t6. Number theory -- $tPart III: Brief survey of NCG -- $t7. Finite geometries -- $t8. Continuous geometries -- $t9. Connes geometries -- $t10. Index theory -- $t11. Jones polynomials -- $t12. Quantum groups -- $t13. Noncommutative algebraic geometry -- $t14. Trends in noncommutative geometry -- $tReferences -- $tIndex 330 $aThis book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field. ContentsPart I: BasicsModel examplesCategories and functorsC?-algebrasPart II: Noncommutative invariantsTopologyAlgebraic geometryNumber theoryPart III: Brief survey of NCGFinite geometriesContinuous geometriesConnes geometriesIndex theoryJones polynomialsQuantum groupsNoncommutative algebraic geometryTrends in noncommutative geometry 410 0$aDe Gruyter studies in mathematics ;$vVolume 66. 606 $aNoncommutative differential geometry 606 $aGeometry, Algebraic 606 $aNumber theory 615 0$aNoncommutative differential geometry. 615 0$aGeometry, Algebraic. 615 0$aNumber theory. 676 $a516.3/5 686 $aSK 240$2rvk 700 $aNikolaev$b Igor$f1961-$059391 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910539691103321 996 $aNoncommutative geometry$92617932 997 $aUNINA