Questions tagged [kirby-calculus]
Kirby diagrams of 4-manifolds, Kirby moves and Kirby calculus, Akbulut diagrams, handle decompositions
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questions with no upvoted or accepted answers
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Kirby diagram of Enriques surface (as the "(1/2) K3 surface")
Not to be confused with $E(1)\cong\mathbb{C}P^2\#9\overline{\mathbb{C}P^2}$, which is also known as a $\frac{1}{2}K3$ surface (in the sense that removing a neighbourhood of a regular torus fiber in $E(...
4
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Kirby's theorem for 4-manifolds
In dimension 3, we have the celebrated Kirby theorem: Let $L_1, L_2$ be two links in the 3-sphere $S^3$; then they surgeries along them produce homeomorphic 3-manifolds if and only if they are related ...
4
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Blow-up and Blow-down kirby local moves for non-orientable $3$-manifold
Can anyone explain or give a reference about the Blow-up and Blow-down Kirby local moves for non-orientable $3$-manifolds?
Thanks, advance.
4
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Cap product for (co)homology from handle decompositions/Kirby diagrams
Since handle decompositions and Morse functions are intimately related, I'm imagining that a given explicit handle decomposition allows for an explicit description of the cellular complex and thus of (...
3
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What's a completely computational/syntactical model for handle decompositions of manifolds?
Simplicial sets, CW complexes
Simplicial sets can be described completely algebraically, by specifying a family of sets, and maps between them satisfying certain relations. This description can be ...
2
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Homotopy type of a 3-manifold produced via Dehn surgery?
My apologizes if this is a fairly elementary question, I am still a novice when it comes to 3-manifold topology.
I am wondering the following: by Kirby calculus, we know that two links (say in $S^{3}$ ...
2
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173
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The Kirby diagram of a manifold glued along the lens space $L(p,1)$
Suppose $K$ is a knot in $S^3$ with any framing and $m=m_0$ is its meridian with $-1$ framing. Suppose $m_1,\dots,m_{p-1}$ are unknots with framings $-2$, such that $m_{i-1}$ and $m_i$ are linked as a ...
2
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Tubular neighbourhoods are unique up to ambient isotopy?
Let $M$ be a closed smooth submanifold of $N$. It is well known that tubular neigbourhoods of $M$ are diffeomorphic to the normal bundle of $M$ in $N$ and therefore to each other. Are they smoothly ...
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Mapping class group and surgery theory
Given a smooth manifold $M$ of dimension $n$ and a diffeomorphism $\phi: M \to M$, we can construct a smooth cobordism of dimension $(n+1)$ from $M$ to $M$ by gluing $M \times [0,1]$ with itself by $\...