Parallel forms, co-K\"ahler Manifolds and their Models

TL;DR

This paper explores the topological and cohomological properties of co-K"ahler manifolds, demonstrating how their structure simplifies cohomology calculations and confirms their formality, based on properties inherited from K"ahler manifolds.

Contribution

It establishes a connection between co-K"ahler and K"ahler manifolds, providing a new approach to compute cohomology and proving formality of the foliation minimal model.

Findings

Cohomology computation reduces to natural sub-cdga's

Existence of parallel forms simplifies topological analysis

Provides a new proof of formality for co-K"ahler manifolds

Abstract

We show how certain topological properties of co-K\"ahler manifolds derive from those of the K\"ahler manifolds which construct them. In particular, we show that the existence of parallel forms on a co-K\"ahler manifold reduces the computation of cohomology from the de Rham complex to certain amenable sub-cdga's defined by geometrically natural operators derived from the co-K\"ahler structure. This provides a simpler proof of the formality of the foliation minimal model in this context.