The totally nonnegative Grassmannian is a ball

TL;DR

This paper proves that three significant spaces in topological combinatorics—the totally nonnegative Grassmannian, the compactification of electrical networks, and the cyclically symmetric amplituhedron—are all homeomorphic to closed balls, revealing their topological simplicity.

Contribution

It establishes the homeomorphism of these three important spaces to closed balls, providing new insights into their topological structure.

Findings

The totally nonnegative Grassmannian is homeomorphic to a closed ball.

The compactification of electrical networks is homeomorphic to a closed ball.

The cyclically symmetric amplituhedron is homeomorphic to a closed ball.

Abstract

We prove that three spaces of importance in topological combinatorics are homeomorphic to closed balls: the totally nonnegative Grassmannian, the compactification of the space of electrical networks, and the cyclically symmetric amplituhedron.