A K-theoretic interpretation of real Deligne cohomology

TL;DR

This paper reveals that real Deligne cohomology can be understood as a topological completion of the Lie groupoid of holomorphic vector bundles, connecting K-theory and Beilinson's regulator.

Contribution

It provides a K-theoretic interpretation of real Deligne cohomology, linking it to the analytic Lie groupoid of holomorphic vector bundles.

Findings

Real Deligne cohomology arises as a topological vector space completion.

Beilinson's regulator naturally appears as a comparison map between K-theory groups.

The work bridges K-theory, complex geometry, and cohomological theories.

Abstract

We show that real Deligne cohomology of a complex manifold arises locally as a topological vector space completion of the analytic Lie groupoid of holomorphic vector bundles. Thus Beilinson's regulator arises naturally as a comparison map between $K$-theory groups of different types.