Weight decompositions on algebraic models for mapping spaces and homotopy automorphisms

TL;DR

This paper uses positive weight decompositions to analyze the rational homotopy types of mapping spaces and automorphism classifying spaces, with applications to Kähler manifolds and holomorphic maps.

Contribution

It introduces restrictions on rational homotopy types using weight decompositions, extending to holomorphic maps and automorphisms of Kähler manifolds.

Findings

Restrictions on rational homotopy types of mapping spaces

Applications to holomorphic maps between Kähler manifolds

Insights into homotopy automorphisms of Kähler manifolds

Abstract

We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components of holomorphic maps between compact K\"ahler manifolds as well as homotopy automorphisms of K\"ahler manifolds.