All Questions
7 questions
4
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1
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Question about the fundamental group of rational homology 3-spheres
By a rational homology 3-sphere, I mean a compact oriented manifold three-manifold $Y$ with $H_1(Y)$ finite. My question is whether there exists a reasonable classification of such manifolds such that ...
- 68.9k
3
votes
0
answers
58
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What's the Milnor's link group for the trivial knot in a lens space?
For a link $L$ in a 3-manifold $Y$, Milnor's paper "Link Groups" https://link.springer.com/content/pdf/10.1007/BF01393902.pdf defined the link group as some quotient of $\pi_1(Y-L)$. If $L$ ...
- 673
4
votes
0
answers
397
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Contractibility and orientation double cover
Question. Let $M$ be a triangulated non-orientable 3-manifold with non-orientable boundary. (It is possible to assume that the boundary is the Klein bottle.) Let $\ell$ be a non-orientable loop on the ...
- 976
5
votes
1
answer
353
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Fundamental groups of open sets in $R^n$ with $n=3,4$
It is well known that every finitely presented group may be realised as fundamental group of some closed $4$-manifold.
What groups can be obtained as fundamental groups of open subsets of $R^4$? I'...
- 96.4k
5
votes
1
answer
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On the fundamental group of closed 3-manifolds
I know that every finitely presented group can be realized as the fundamental group of a compact, connected, smooth manifold of dimension 4 (or higher). In dimension 2 there are strong restriction on ...
- 5,259
7
votes
2
answers
2k
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The fundamental group of a $3$-manifold with a boundary of genus $>0$
Let $M$ be an orientable $3$-manifold with connected boundary $\Sigma_g$, a surface of genus $g>0$.
I would like to find a reference to the following two statements.
1) $\pi_1(M)\ne 0$.
2) $\...
- 31.2k
4
votes
2
answers
1k
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Fundamental groups of closed hyperbolic 3-manifolds are freely indecomposable
I believe the following statement is true, and I've even seen it referenced here. Could someone point me to a proof?
The fundamental group of a closed hyperbolic 3-manifold is not a free product.
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