New answers tagged 3-manifolds
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4-manifold obtained from a ribbon disk exterior by attaching a 2-handle is simply-connected if its boundary is a homology sphere
This is false in general, I’ll prove the existence of a counterexample.
Since $D$ is a ribbon disk, $X$ has a handle structure with one $0$-handle, $n$ $1$-handles and $n-1$ $2$-handles (as described ...
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6
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Small examples of exceptional hyperbolic Dehn Filling of hyperbolic manifolds
Here is a variant of Ian's answer. We cut along the round component in his diagram, perform a full twist (with the correct handedness), and reglue. This gives the following three-component link.
If ...
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7
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Small examples of exceptional hyperbolic Dehn Filling of hyperbolic manifolds
Another sort of example is a geodesic that is not embedded. In the Whitehead link complement, there is a thrice-punctured sphere (pants) which is totally geodesic. A figure 8 curve in such a surface ...
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9
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Small examples of exceptional hyperbolic Dehn Filling of hyperbolic manifolds
Here are two examples of exceptional hyperbolic fillings. In the first the core curve becomes parabolic after filling (so cannot be isotopic to a geodesic). In the second, the core curve is homotopic (...
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Pullback of $w_1$ for 3-manifolds
For manifolds $M,N$ of dimension $<3$ I know the complete answer for the similar question.
If $M,N$ are closed $1$-manifolds, obviously, $f$ exists if and only if $\alpha=0$.
If $M,N$ are closed $...
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Pullback of $w_1$ for 3-manifolds
This basically boils down to
Understanding what the class $w_1$ represents, and
Doing obstruction theory.
This is generally not an easy question to answer, since obstruction theory requires you to ...
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Accepted
0-framed smoothly slice knot that can be obtained by blowing down successively a link of unknots
Yes, you can always do this. In fact, I think you can do it for any framed link, regardless of the framings, the number of components, and the slice assumption. (For simplicity, I will write the ...
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