LEADER 04112nam 2200673 a 450 001 9910810317203321 005 20200520144314.0 010 $a1-281-49124-1 010 $a9786611491246 010 $a3-7643-8775-0 024 7 $a10.1007/978-3-7643-8775-4 035 $a(CKB)1000000000440910 035 $a(EBL)367337 035 $a(OCoLC)272313415 035 $a(SSID)ssj0000145541 035 $a(PQKBManifestationID)11165442 035 $a(PQKBTitleCode)TC0000145541 035 $a(PQKBWorkID)10156930 035 $a(PQKB)11611159 035 $a(DE-He213)978-3-7643-8775-4 035 $a(MiAaPQ)EBC367337 035 $a(Au-PeEL)EBL367337 035 $a(CaPaEBR)ebr10239484 035 $a(CaONFJC)MIL149124 035 $a(PPN)127052836 035 $a(EXLCZ)991000000000440910 100 $a20081202d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aElliptic theory and noncommutative geometry $enonlocal elliptic operators /$fVladimir E. Nazaikinskii, Anton Yu. Savin, Boris Yu. Sternin 205 $a1st ed. 2008. 210 $aBasel $cBirkha?user$d2008 215 $a1 online resource (232 p.) 225 1 $aOperator theory, advances and applications$aAdvances in partial differential equations ;$vv. 183 300 $aDescription based upon print version of record. 311 $a3-7643-8774-2 320 $aIncludes bibliographical references and index. 327 $aAnalysis of Nonlocal Elliptic Operators -- Nonlocal Functions and Bundles -- Nonlocal Elliptic Operators -- Elliptic Operators over C*-Algebras -- Homotopy Invariants of Nonlocal Elliptic Operators -- Homotopy Classification -- Analytic Invariants -- Bott Periodicity -- Direct Image and Index Formulas in K-Theory -- Chern Character -- Cohomological Index Formula -- Cohomological Formula for the ?-Index -- Index of Nonlocal Operators over C*-Algebras -- Examples -- Index Formula on the Noncommutative Torus -- An Application of Higher Traces -- Index Formula for a Finite Group ?. 330 $aThis comprehensive yet concise book deals with nonlocal elliptic differential operators, whose coefficients involve shifts generated by diffeomorophisms of the manifold on which the operators are defined. The main goal of the study is to relate analytical invariants (in particular, the index) of such elliptic operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. This is the first and so far the only book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. Although the book provides important results, which are in a sense definitive, on the above-mentioned topic, it contains all the necessary preliminary material, such as C*-algebras and their K-theory or cyclic homology. Thus the material is accessible for undergraduate students of mathematics (third year and beyond). It is also undoubtedly of interest for post-graduate students and scientists specializing in geometry, the theory of differential equations, functional analysis, etc. The book can serve as a good introduction to noncommutative geometry, which is one of the most powerful modern tools for studying a wide range of problems in mathematics and theoretical physics. 410 0$aOperator theory, advances and applications ;$vv. 183. 410 0$aOperator theory, advances and applications.$pAdvances in partial differential equations. 606 $aElliptic operators 606 $aNoncommutative differential geometry 615 0$aElliptic operators. 615 0$aNoncommutative differential geometry. 676 $a515.7242 700 $aNazai?kinskii?$b V. E$0497463 701 $aSavin$b Anton Yu$0310981 701 $aSternin$b B. I?U$01604247 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910810317203321 996 $aElliptic theory and noncommutative geometry$94021325 997 $aUNINA