All the shapes of spaces: a census of small 3-manifolds

TL;DR

This paper provides a comprehensive census of small 3-manifolds using blinks, a universal encoding linked to blackboard framed links, up to 9 edges, aiding in the systematic study of these spaces.

Contribution

It introduces a complete census of prime 3-manifolds via blinks, establishing a new systematic catalog for small 3-manifolds up to 9 edges.

Findings

Complete census of 3-manifolds up to 9 edges

Blinks as a universal encoding for these manifolds

Establishment of a systematic catalog for future research

Abstract

In this work we present a complete (no misses, no duplicates) census for closed, connected, orientable and prime 3-manifolds induced by plane graphs with a bipartition of its edge set (blinks) up to $k=9$ edges. Blinks form a universal encoding for such manifolds. In fact, each such a manifold is a subtle class of blinks, \cite{lins2013B}. Blinks are in 1-1 correpondence with {\em blackboard framed links}, \cite {kauffman1991knots, kauffman1994tlr} We hope that this census becomes as useful for the study of concrete examples of 3-manifolds as the tables of knots are in the study of knots and links.