# Homotopically rigid Sullivan algebras and Their applications

## TL;DR

This paper constructs homotopically rigid spaces and uses them to create highly connected rational spaces with specific symmetry properties, as well as inflexible and chiral manifolds, advancing understanding in rational homotopy theory.

## Contribution

It introduces an infinite family of homotopically rigid spaces and applies them to build highly connected rational spaces and manifolds with prescribed symmetries.

## Key findings

- Constructed an infinite family of homotopically rigid spaces
- Developed highly connected rational spaces with finite self-homotopy groups
- Produced highly connected inflexible and strongly chiral manifolds

## Abstract

In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescribed finite group of self-homotopy equivalences. They are also exploited to provide highly connected inflexible and strongly chiral manifolds.