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Asymptotic Cyclic Cohomology

Michael Puschnigg (Autor)

Buch | Softcover

XXIV, 244 Seiten

1996
Springer Berlin (Verlag)
978-3-540-61986-4 (ISBN)

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The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups.

The asymptotic homotopy category.- Algebraic de Rham complexes.- Cyclic cohomology.- Homotopy properties of X-complexes.- The analytic X-complex.- The asymptotic X-complex.- Asymptotic cyclic cohomology of dense subalgebras.- Products.- Exact sequences.- KK-theory and asymptotic cohomology.- Examples.

Erscheint lt. Verlag	16.12.1996
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XXIV, 244 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	345 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	cohomology • Cohomology group • Cohomology theory • de Rham cohomology • Homologische Algebra • Homology • Homotopy • Index Theory • Kohomologie • K-Theorie • K-theory • noncomutative geometry
ISBN-10	3-540-61986-0 / 3540619860
ISBN-13	978-3-540-61986-4 / 9783540619864
Zustand	Neuware