# Fibrations and higher products in cohomology

## TL;DR

This paper explores the relationship between fibrations with finite homological dimension fibers and higher products in cohomology within the framework of commutative differential graded algebras, extending previous work with Sullivan.

## Contribution

It identifies cohomology classes annihilated by specific fibrations with higher products, advancing understanding of their algebraic structure.

## Key findings

- Cohomology classes can be characterized by higher products.
- Fibrations with finite homological dimension relate to specific cohomology classes.
- Extension of previous work with Sullivan on algebraic topology.

## Abstract

This paper is a continuation of a previous paper joint with Dennis Sullivan (arXiv:1704.04308). Working in the context of commutative differential graded algebras, we study the ideal of the cohomology classes which can be annihilated by fibrations whose fiber has finite homological dimension. In the present paper we identify these classes with certain higher products in cohomology.