Questions tagged [handle-decomposition]
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6
questions with no upvoted or accepted answers
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Questions about a paper by Laudenbach and Poénaru
I am working on the 1972 paper A Note on 4-Dimensional Handlebodies by F. Laudenbach and V. Poénaru, and I had two questions. I will use their notations to simplify things, since the paper is very ...
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Handle attachment in symplectic category
It is known that for an exact symplectic manifold $(M,\omega_M)$ with a convex boundary $(\partial M,\theta_M)$, where $d\theta_M=\omega_M$ (usually called a Liouville domain), one can attachment to ...
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 ...
3
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Is complex surface in CP(3) a two handlebody?
Consider a complex surface given by homogeneous equation in $\mathbb{C}P^3$. Without loss of generality, take
\begin{equation}
S = \{[x:y:z:w] \in \mathbb{C}P^3~ |~ x^d + y^d + z^d + w^d = 0\}
\end{...
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Attaching a 2-handle to a once-twisted unlink in the boundary of the 4-ball
Consider the 3-sphere $S_3$ with an unlink loop $L$ whose tubular neighborhood is identified with the solid torus $B_2\times S_1$ with one twist, i.e., such that the image of $x\times S_1$ (where $x$ ...