Homology, Homotopy and Applications

Volume 7 (2005)

Number 3

Proceedings of a Conference in honour of Victor Snaith

Additivity of Euler characteristics in relative algebraic $K$-groups

Pages: 11 – 36

DOI: https://dx.doi.org/10.4310/HHA.2005.v7.n3.a2

Authors

Manuel Breuning (School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom)

David Burns (Department of Mathematics, King’s College London, United Kingdom)

Abstract

We describe a criterion for a natural Euler characteristic that takes values in a relative algebraic $K_0$-group to be additive in distinguished triangles. As preliminary steps we prove several results about determinant functors, in particular concerning the comparison of the determinant of a complex to the determinant of its cohomology.

Keywords

determinant functors, Euler characteristics, relative algebraic $K$-groups

2010 Mathematics Subject Classification

16E20, 18D10, 18E10, 18E30

Published 1 January 2005