Journal Article10.2307/1970373
A Representation of Orientable Combinatorial 3-Manifolds
TL;DR: In this paper, it was shown that every closed, connected, orientable, 3-manifold is obtainable from S3 in the same way as shown in this paper.
read more
Abstract: The following question has been posed by Bing [1]: "Which compact, connected 3-manifolds can be obtained from S3 as follows: Remove a finite collection of mutually exclusive (but perhaps knotted and linking) polyhedral tori T1, T2, * *, To from S3, and sew them back. " This paper answers that question by showing that every closed, connected, orientable, 3-manifold is obtainable from S3 in the above way. Whereas this fact can now be deduced from general theorems of differential topology, the combinatorial proof given here is direct and elementary; while, in the proof, a study is made of a certain type of homeomorphism of a two dimensional manifold that is of interest in itself. Having obtained the above mentioned result on 3-manifolds, it is then easy to deduce the well known result (Theorem 3) that the combinatorial cobordism group for orientable 3-manifolds is trivial.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Closed, oriented, connected 3-manifolds are subtle equivalence classes of plane graphs
Sóstenes Lins,Diogo B. Henriques +1 more
TL;DR: In this article, it was shown that the homeomorphisms classes of closed oriented 3-manifolds are in 1-1 correspondence with speci c classes of blinks, where two blinks are equivalent if they are linked by a sequence of local moves, where each one appears in a concrete list of 64 moves: they organize in 8 types, each being essentially the same move on 8 simply related con gurations.
2
Studies of distance one surgeries on the lens space L(p, 1)
Zhongtao Wu,Jingling Yang +1 more
- 07 Jun 2021
TL;DR: It is proved that L(n, 1) is obtained by a distance one surgery from L(5,1) only if and only if n=±1, 4, ±5, 6 or ±9.
2
On volumes and filling collections of multicurves
20 Jun 2022
TL;DR: In this article , it was shown that the Weil-Petersson distance between strata in Teichmüller space is coarsely comparable to the distance in the pants graph.
2
•Dissertation
Combinatorial width parameters for 3-dimensional manifolds
Kristóf Huszár
- 01 Jan 2020
TL;DR: This thesis establishes quantitative relations between the treewidth and classical topological invariants of a 3-manifold, and shows that thetreewidth of a closed, orientable, irreducible, non-Haken 3- manifold is always within a constant factor of its Heegaard genus.
•Posted Content
Transformation Optics for the Modelling of Waves in a Universe with Nontrivial Topology
TL;DR: In this article, transformation optics and invisibility cloaking can be used to construct models in subsets of the Riemannian manifold, where the time-harmonic waves for a given angular wavenumber $k$ are equivalent to the waves in some closed orientable manifold.
2