Hardcover ISBN:  9783037190609 
Product Code:  EMSSCR/2 
List Price:  $124.00 
AMS Member Price:  $99.20 
Hardcover ISBN:  9783037190609 
Product Code:  EMSSCR/2 
List Price:  $124.00 
AMS Member Price:  $99.20 

Book DetailsEMS Series of Congress ReportsVolume: 2; 2008; 454 ppMSC: Primary 19; 58; 14; 46; 53
Since its inception 50 years ago, Ktheory has been a tool for understanding a wideranging 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 Ktheory 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 Ktheory, 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 Ktheory. There are primary and secondary Chern characters which pass from Ktheory 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 Ktheory, noncommmutative geometry, and other branches of mathematics.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
ReadershipGraduate students and research mathematicians interested in Ktheory and noncommutative geometry.

RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Requests
Since its inception 50 years ago, Ktheory has been a tool for understanding a wideranging 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 Ktheory 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 Ktheory, 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 Ktheory. There are primary and secondary Chern characters which pass from Ktheory 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 Ktheory, noncommmutative geometry, and other branches of mathematics.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Graduate students and research mathematicians interested in Ktheory and noncommutative geometry.