All the shapes of spaces: a census of small 3-manifolds
S\'ostenes L. Lins, Lauro D. Lins

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 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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology
