# Connected Projections of Configuration Spaces of Linkages

## TL;DR

This paper demonstrates that any compact connected semialgebraic set can be represented as a projection of a connected component of a linkage's configuration space, linking geometric structures with mechanical linkages.

## Contribution

It establishes a universal representation of semialgebraic sets via linkage configuration spaces, bridging geometry and mechanical linkages.

## Key findings

- Any compact connected semialgebraic set is realizable as a projection of a linkage configuration space.
- The result connects geometric set theory with the topology of linkage configurations.
- Provides a method to construct linkages for arbitrary semialgebraic sets.

## Abstract

We show that any compact connected semialgebraic set is the projection of a connected component of the configuration space of a linkage.