# Examples of foliations with infinite dimensional special cohomology

## TL;DR

This paper provides examples of foliations exhibiting infinite dimensional basic symplectic and complex cohomologies, highlighting limitations on extending finiteness results from Riemannian foliations to broader classes.

## Contribution

It introduces specific examples of foliations with infinite dimensional cohomologies and a general condition for such phenomena, challenging existing finiteness assumptions.

## Key findings

- Examples of foliations with infinite dimensional cohomologies
- A general sufficient condition for infinite dimensionality
- Unusual behavior of basic de Rham cohomology

## Abstract

We present examples of foliations with infinite dimensional basic symplectic and com- plex cohomologies, along with a general sufficient condition for such phenomena. This puts re- strictions on possible generalizations of several finiteness results from Riemannian foliations to any broader class. The examples are also noteworthy for the unusual behaviour of their basic de Rham cohomology.