Self-replicating 3-manifolds

TL;DR

This paper classifies self-replicating 3-manifolds using topological and categorical methods, and explores their embeddings in three-dimensional space, revealing new insights into their structure and biological relevance.

Contribution

It provides a classification theorem for self-replicating 3-manifolds modeled by idempotents in the cobordism category and characterizes their embeddings in Euclidean space.

Findings

Classification of all such idempotents

Characterization of embeddings in $ extbf{R}^3$

Insights into biological relevance of self-replicating manifolds

Abstract

In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in the (2+1)-cobordism category. We give a classification theorem for all such idempotents. Additionally, we characterize biologically interesting ways in which self-replicating 3-manifolds can embed in $\mathbb{R}^3$.