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Questions tagged [3-manifolds]

A 3-manifold is a space that locally looks like Euclidean 3-dimensional space

375 questions
92 views

Book recommendations beyond an introduction [on hold]

So I’ve scraped the surface of many topics, but I would like to go further. Can anyone recommend some continuations to the following introductory books? It’s okay if necessarily it needs to be a ...
60 views

Circle bundles and surface bundles which admit no strongly irreducible Heegaard splittings

Let $S$ be a closed connected orientable surface with $g(S)>0$. Jennifer Schultens, in her paper The Classification of Heegaard Splittings for (Compact Orientable Surface)$\times S^1$'', proves ...
110 views

SnapPy isometry routine

Dear Colleagues and Friends, Here's a question that I hope some of you, more experienced in programming, can answer. Once SnapPy is used to compute the symmetry group of a hyperbolic manifold by ...
87 views

Existence of smooth structures on topological $3$-manifolds with boundary

It is said in this thread Unique smooth structure on $3$-manifolds that every topological $3$-manifold admits a smooth structure. However it is not specified whether the manifolds are allowed to have ...
228 views

open book decompositions of $\Sigma\times S^1$

Let $\Sigma$ be a closed orientable surface. Is there a standard open book decomposition on the $3$-manifold $M=\Sigma\times S^1$? If the binding is allowed to be empty in the definition of an open ...
178 views

Triangulations of 3-manifolds in Regina and SnapPy

I have been doing some statistical studies on small 3-manifolds, and I note that one can produce larg-ish censuses of triangulations in Regina. Now, the Regina documentation tells us how to convert a ...
126 views

Let $M$ be a closed hyperbolic 3-manifold. One can use hyperbolic structure on $M$ to define hyperbolic volume $Vol(M)$. Thanks to Mostow's rigidity theorem the volume depends only on the topology of ...
44 views

Surgery (Kirby) diagram of connected sum of lens spaces?

What is the kirby/surgery diagram for a connected sum of two lens spaces? Question 1: is it just the unlink with $p/q$ coefficients? Question 2: if not, what manifold is the unlink with $p_i/q_i$ ...
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3d Chern-Simons TQFT of gauge group (E8)$_1$ = SO(16)$_1 \otimes$ a trivial spin TQFT = Cartan E$_8$ matrix

In this post, we like to relate the following 3 bosonic TQFTs that can be defined on generic non-spin manifold $M^3$. Given a non-abelian Chern-Simons (CS) TQFT of a gauge group $G$ and the $k$ named ...
82 views

Manifold with no closed components?

Let $M$ be a manifold with boundary. Reading some papers on $3$-manifolds I have come across some statements where they require that: ”$M$ has no closed components.” What does this mean? The ...
157 views

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Reference request for wild 3-manifolds

I’m looking for a text on 3-manifolds that focuses on wild/pathological objects, similar to Bing’s work in the field. I know basic algebraic topology (homotopy, homology, cohomology) and have read ...

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