Euler characteristic and the class of unit in K-theory
type: Item
instance of: scholarly article
title: Euler characteristic and the class of unit in K-theory
zbMATH Open document ID: 0594.57010
DOI: 10.1007/BF01161971
author: Natsume Toshikazu
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173830
review text: Let \(\chi (\xi_{\phi})\) be the Euler characteristic of the \(S^ 1\)- bundle over a compact Riemannian surface \(M_ g\) of genus \(g\geq 2\) associated to an arbitrary homomorphism \(\phi\) from \(\pi_ 1(M_ g)\) into the group \(Top_+(S^ 1)\) of all orientation preserving homeomorphisms of \(S^ 1\). Then, in the \(K_ 0\)-group of the reduced crossed product \(C(S^ 1)\rtimes \pi_ 1(M_ g)\), the class of unit [1] is a torsion element with \(\chi (\xi_{\phi})[1]=0\).
Mathematics Subject Classification ID: 57R22
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 3956004
zbMATH Keywords: Euler characteristic of an \(S^ 1\)-bundle over a compact Riemannian surface
zbMATH Keywords: \(K_ 0\)-group of reduced crossed product
zbMATH Keywords: projective class group
MaRDI profile type: Publication
cites work: Q3791701
cites work: A Bott periodicity map for crossed products of C *-algebras by discrete groups
cites work: Q4725183
cites work: Q3930248
cites work: Q3316025
cites work: Bundles with totally disconnected structure group
cites work: Q3736365
OpenAlex ID: W2031221108
description: scientific article; zbMATH DE number 3956004