On operations and characteristic classes

TL;DR

This paper introduces a new framework using exterior products to define operations and characteristic classes within the K-theory of abelian categories, applying it to algebraic and connection K-theories.

Contribution

It develops a general construction for characteristic classes in K-theory using exterior products, extending their application to algebraic and connection K-theories.

Findings

Defined Chern and Segre classes in algebraic K-theory

Established operations in K-theory of an abelian category

Unified approach to characteristic classes in different K-theories

Abstract

In this paper exterior products are used to define operations and characteristic classes with values in the K-theory of an abelian category with tensor and exterior products. We apply the general construction to define Chern and Segre classes with values in algebraic K-theory and the K-theory of connections.