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Local and analytic cyclic homology /

Meyer, Ralf.

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Local and analytic cyclic homology /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Local and analytic cyclic homology // Ralf Meyer.
Author:	Meyer, Ralf.
Published:	Zürich :European Mathematical Society, : c2007.,
Description:	viii, 360 p. :ill. ;25 cm.
Subject:	Algebra, Homological. -
ISBN:	9783037190395 (hbk.) :

Local and analytic cyclic homology /
Meyer, Ralf.

Local and analytic cyclic homology /Ralf Meyer. - Zürich :European Mathematical Society,c2007. - viii, 360 p. :ill. ;25 cm. - EMS tracts in mathematics ;v3. - EMS tracts in mathematics ;11..

Includes bibliographical references (p. [343]-348) and index.

"Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book, the author develops and compares these theories, emphasizing their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to K-theory, and the Chern-Connes character for K-theory and K-homology." "The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras." "This book is mainly intended for researchers and advanced graduate students interested in non-commutative geometry. Some chapters are more elementary and independent of the rest of the book and will be of interest to researchers and students working on functional analysis and its applications."--BOOK JACKET.

ISBN: 9783037190395 (hbk.) :US78.00Subjects--Topical Terms:

663850
Algebra, Homological.

LC Class. No.: QA612.3 / .M49 2007

Local and analytic cyclic homology /
LDR:01992cam a2200193 a 4500 001 1266122
003 OCoLC
005 20120724033106.0
008 120822s2007 sz a b 001 0 eng c
020 $a 9783037190395 (hbk.) : $c US78.00
020 $a 3037190396 (hbk.)
035 $a AS-BW-101-N-03
040 $a COO $c COO $d YDXCP $d OCLCQ $d SZ9XM $d STF $d UMR
050 # 4 $a QA612.3 $b .M49 2007
100 1 $a Meyer, Ralf. $3 1042784
245 1 0 $a Local and analytic cyclic homology / $c Ralf Meyer.
260 # $a Zürich : $b European Mathematical Society, $c c2007.
300 $a viii, 360 p. : $b ill. ; $c 25 cm.
490 1 0 $a EMS tracts in mathematics ; $v v3
504 $a Includes bibliographical references (p. [343]-348) and index.
520 1 $a "Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book, the author develops and compares these theories, emphasizing their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to K-theory, and the Chern-Connes character for K-theory and K-homology." "The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras." "This book is mainly intended for researchers and advanced graduate students interested in non-commutative geometry. Some chapters are more elementary and independent of the rest of the book and will be of interest to researchers and students working on functional analysis and its applications."--BOOK JACKET.
650 # 0 $a Algebra, Homological. $3 663850
650 # 0 $a Homology theory. $3 555733
650 # 0 $a Banach algebras. $3 594710
830 0 $a EMS tracts in mathematics ; $v 11. $3 1517269