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

2013/05/24 by Sóstenes L. Lins, Lins, Sóstenes L., Lauro D. Lins +1
Mathematics · #57M25 and 57Q15 (primary) #57M27 and 57M15 (secondary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M15 #msc:57M25 #msc:57M27 #msc:57Q15

paper · pdf · doi:10.48550/arxiv.1305.5590

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

arxiv created 2013/06/07 · arxiv updated 2013/06/10

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, \citelins2013B. 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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