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

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.

31 pages, 17 figures, 38 references. In this version we introduce some new material concerning composite manifolds

References in corpus (7)

• BLINK: a language to view, recognize, classify and manipulate 3D-spaces
• Framed link presentations of 3-manifolds by an {O}(n^2) algorithm, III: geometric complex ${\mathcal{H}}_n^{\star }$ embedded into ${\mathbb{R}}^3$
• Framed link presentations of 3-manifolds by an $O(n^2)$ algorithm, I: gems and their duals
• Framed link presentations of 3-manifolds by an $O(n^2)$ algorithm, II: colored complexes and boundings in their complexity
• A challenge to 3-manifold topologists and group algebraists
• Closed oriented 3-manifolds are subtle equivalence classes of plane graphs
• A tougher challenge to 3-manifold topologists and group algebraists