Fullerenes, Polytopes and Toric Topology

TL;DR

This paper explores the application of toric topology to the study of fullerenes, a class of 3D polytopes relevant in quantum physics and nanotechnology, to develop combinatorial invariants.

Contribution

It introduces how toric topology techniques can be used to analyze and create invariants for fullerenes, linking geometry with quantum chemistry.

Findings

Development of combinatorial invariants for fullerenes

Application of toric topology to polytope analysis

Bridging mathematics with nanotechnology models

Abstract

The lectures are devoted to a remarkable class of $3$-dimensional polytopes, which are mathematical models of the important object of quantum physics, quantum chemistry and nanotechnology -- fullerenes. The main goal is to show how results of toric topology help to build combinatorial invariants of fullerenes. Main notions are introduced during the lectures. The lecture notes are addressed to a wide audience.