Comparison of secondary invariants of algebraic K-theory

TL;DR

This paper demonstrates that two important secondary invariants in algebraic K-theory, the multiplicative character and the determinant invariant, are equivalent up to a canonical homomorphism, unifying their perspectives.

Contribution

It establishes the equivalence of the multiplicative character and the determinant invariant in algebraic K-theory, clarifying their relationship.

Findings

The multiplicative character and the determinant invariant agree up to a canonical homomorphism.

This result unifies two previously distinct secondary invariants.

The proof provides a deeper understanding of algebraic K-theory invariants.

Abstract

In this paper we prove that the multiplicative character of A. Connes and M. Karoubi and the determinant invariant of L. G. Brown, J. W. Helton and R. E. Howe agree up to a canonical homomorphism.