Mutants of compactified representations revisited

TL;DR

This paper revisits mutants of compactified representations, demonstrating their description as intersections of real quadrics involving division algebras, and establishing that these manifolds are connected sums of products of spheres.

Contribution

It provides a new perspective on mutants of compactified representations, linking them to intersections of real quadrics and generalizations of polygon spaces, and characterizes their topological structure.

Findings

Mutants can be expressed as intersections of real quadrics involving division algebras.

These manifolds are connected sums of products of spheres.

The work generalizes polygon spaces and clarifies their topological structure.

Abstract

We show that the mutants of compactified representations constructed by Franz and Puppe can be written as intersections of real quadrics involving division algebras and as generalizations of polygon spaces. We also show that these manifolds are connected sums of products of spheres.