Concepts of polymer statistical topology

TL;DR

This paper reviews the foundational concepts in the analytic description of topological interactions within the emerging field of statistical topology, which combines topology and statistical physics to study fluctuating rope-like objects.

Contribution

It introduces the conceptual framework of statistical topology, bridging topology and statistical physics for analyzing complex topological interactions.

Findings

Defines the core principles of statistical topology

Highlights the interdisciplinary nature of the field

Lays groundwork for future research in topological interactions

Abstract

I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical physics of fluctuating non-phantom rope-like objects. This new branch is called statistical (or probabilistic) topology.