The Kunneth Theorem and the Universal Coefficient Theorem for Equivariant $K$-Theory and $KK$-Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 0821823493
Total Pages : 105 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Kunneth Theorem and the Universal Coefficient Theorem for Equivariant $K$-Theory and $KK$-Theory by : Jonathan Micah Rosenberg

Download or read book The Kunneth Theorem and the Universal Coefficient Theorem for Equivariant $K$-Theory and $KK$-Theory written by Jonathan Micah Rosenberg and published by American Mathematical Soc.. This book was released on 1986 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: "July 1986, volume 62, number 348 (second of 6 numbers)."

The Künneth Theorem and the Universal Coefficient Theorem for Equivariant K-theory and KK-theory

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Publisher :
ISBN 13 : 9781470407643
Total Pages : 0 pages
Book Rating : 4.4/5 (76 download)

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Book Synopsis The Künneth Theorem and the Universal Coefficient Theorem for Equivariant K-theory and KK-theory by : Jonathan Micah Rosenberg

Download or read book The Künneth Theorem and the Universal Coefficient Theorem for Equivariant K-theory and KK-theory written by Jonathan Micah Rosenberg and published by . This book was released on 1986 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The KŸnneth Theorem and the Universal Coefficient Theorem for Equivariant K-theory and KK-theory

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821860809
Total Pages : 106 pages
Book Rating : 4.8/5 (68 download)

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Book Synopsis The KŸnneth Theorem and the Universal Coefficient Theorem for Equivariant K-theory and KK-theory by : Jonathan R_osenberg

Download or read book The KŸnneth Theorem and the Universal Coefficient Theorem for Equivariant K-theory and KK-theory written by Jonathan R_osenberg and published by American Mathematical Soc.. This book was released on 1986-12-31 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Universal Coefficient Theorem and Quantum Field Theory

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Publisher : Springer
ISBN 13 : 3319461435
Total Pages : 279 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis The Universal Coefficient Theorem and Quantum Field Theory by : Andrei-Tudor Patrascu

Download or read book The Universal Coefficient Theorem and Quantum Field Theory written by Andrei-Tudor Patrascu and published by Springer. This book was released on 2016-09-23 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

K-Theory for Operator Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 1461395720
Total Pages : 347 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis K-Theory for Operator Algebras by : Bruce Blackadar

Download or read book K-Theory for Operator Algebras written by Bruce Blackadar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.

K-theory and Noncommutative Geometry

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Publisher : European Mathematical Society
ISBN 13 : 9783037190609
Total Pages : 460 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis K-theory and Noncommutative Geometry by : Guillermo Cortiñas

Download or read book K-theory and Noncommutative Geometry written by Guillermo Cortiñas and published by European Mathematical Society. This book was released on 2008 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 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.

Equivariant K-Theory and Freeness of Group Actions on C*-Algebras

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Publisher : Springer
ISBN 13 : 354047868X
Total Pages : 380 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Equivariant K-Theory and Freeness of Group Actions on C*-Algebras by : N. Christopher Phillips

Download or read book Equivariant K-Theory and Freeness of Group Actions on C*-Algebras written by N. Christopher Phillips and published by Springer. This book was released on 2006-11-15 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Freeness of an action of a compact Lie group on a compact Hausdorff space is equivalent to a simple condition on the corresponding equivariant K-theory. This fact can be regarded as a theorem on actions on a commutative C*-algebra, namely the algebra of continuous complex-valued functions on the space. The successes of "noncommutative topology" suggest that one should try to generalize this result to actions on arbitrary C*-algebras. Lacking an appropriate definition of a free action on a C*-algebra, one is led instead to the study of actions satisfying conditions on equivariant K-theory - in the cases of spaces, simply freeness. The first third of this book is a detailed exposition of equivariant K-theory and KK-theory, assuming only a general knowledge of C*-algebras and some ordinary K-theory. It continues with the author's research on K-theoretic freeness of actions. It is shown that many properties of freeness generalize, while others do not, and that certain forms of K-theoretic freeness are related to other noncommutative measures of freeness, such as the Connes spectrum. The implications of K-theoretic freeness for actions on type I and AF algebras are also examined, and in these cases K-theoretic freeness is characterized analytically.

$C^*$-Algebras: 1943-1993

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Publisher : American Mathematical Soc.
ISBN 13 : 0821851756
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis $C^*$-Algebras: 1943-1993 by :

Download or read book $C^*$-Algebras: 1943-1993 written by and published by American Mathematical Soc.. This book was released on 1994 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Cumulative Book Index

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Publisher :
ISBN 13 :
Total Pages : 2056 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Cumulative Book Index by :

Download or read book The Cumulative Book Index written by and published by . This book was released on 1988 with total page 2056 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology

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Publisher : Cambridge University Press
ISBN 13 : 052136843X
Total Pages : 257 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology by : David E. Evans

Download or read book Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology written by David E. Evans and published by Cambridge University Press. This book was released on 1988 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.

Cumulative Book Index

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Publisher :
ISBN 13 :
Total Pages : 2056 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Cumulative Book Index by :

Download or read book Cumulative Book Index written by and published by . This book was released on 1988 with total page 2056 pages. Available in PDF, EPUB and Kindle. Book excerpt: A world list of books in the English language.

Equivariant $E$-Theory for $C^*$-Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 0821821164
Total Pages : 101 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Equivariant $E$-Theory for $C^*$-Algebras by : Erik Guentner

Download or read book Equivariant $E$-Theory for $C^*$-Algebras written by Erik Guentner and published by American Mathematical Soc.. This book was released on 2000 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space

Topics in Noncommutative Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 0821868640
Total Pages : 289 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topics in Noncommutative Geometry by : Guillermo Cortiñas

Download or read book Topics in Noncommutative Geometry written by Guillermo Cortiñas and published by American Mathematical Soc.. This book was released on 2012 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Luis Santalo Winter Schools are organized yearly by the Mathematics Department and the Santalo Mathematical Research Institute of the School of Exact and Natural Sciences of the University of Buenos Aires (FCEN). This volume contains the proceedings of the third Luis Santalo Winter School which was devoted to noncommutative geometry and held at FCEN July 26-August 6, 2010. Topics in this volume concern noncommutative geometry in a broad sense, encompassing various mathematical and physical theories that incorporate geometric ideas to the study of noncommutative phenomena. It explores connections with several areas including algebra, analysis, geometry, topology and mathematical physics. Bursztyn and Waldmann discuss the classification of star products of Poisson structures up to Morita equivalence. Tsygan explains the connections between Kontsevich's formality theorem, noncommutative calculus, operads and index theory. Hoefel presents a concrete elementary construction in operad theory. Meyer introduces the subject of $\mathrm{C}^*$-algebraic crossed products. Rosenberg introduces Kasparov's $KK$-theory and noncommutative tori and includes a discussion of the Baum-Connes conjecture for $K$-theory of crossed products, among other topics. Lafont, Ortiz, and Sanchez-Garcia carry out a concrete computation in connection with the Baum-Connes conjecture. Zuk presents some remarkable groups produced by finite automata. Mesland discusses spectral triples and the Kasparov product in $KK$-theory. Trinchero explores the connections between Connes' noncommutative geometry and quantum field theory. Karoubi demonstrates a construction of twisted $K$-theory by means of twisted bundles. Tabuada surveys the theory of noncommutative motives.

Referativnyĭ zhurnal

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Publisher :
ISBN 13 :
Total Pages : 632 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Referativnyĭ zhurnal by :

Download or read book Referativnyĭ zhurnal written by and published by . This book was released on 1987 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topological and Bivariant K-Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 3764383984
Total Pages : 268 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Topological and Bivariant K-Theory by : Joachim Cuntz

Download or read book Topological and Bivariant K-Theory written by Joachim Cuntz and published by Springer Science & Business Media. This book was released on 2007-07-19 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.

Novye inostrannye knigi, vypisannye BAN SSSR v ... godu

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Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (51 download)

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Book Synopsis Novye inostrannye knigi, vypisannye BAN SSSR v ... godu by :

Download or read book Novye inostrannye knigi, vypisannye BAN SSSR v ... godu written by and published by . This book was released on 1989 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Scientific and Technical Books and Serials in Print

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Publisher :
ISBN 13 :
Total Pages : 1216 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Scientific and Technical Books and Serials in Print by :

Download or read book Scientific and Technical Books and Serials in Print written by and published by . This book was released on 1989 with total page 1216 pages. Available in PDF, EPUB and Kindle. Book excerpt: