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Results tagged with surgery-theory
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user 156537
In geometric topology, surgery theory is used to produce one finite-dimensional manifold from another in a 'controlled' way. Originally developed for differentiable (smooth) manifolds, surgery techniques also apply to piecewise linear and topological manifolds. Surgery refers to cutting out parts of the manifold and replacing it with a part of another manifold, matching up along the cut or boundary. This is related to handlebody decompositions.
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Gluing a manifold along its boundary, via chain complexes
Given closed oriented $n$-manifolds $M, M', M''$ and bordisms $W, W'$ with $\partial W = M \sqcup - M'$ and $\partial W' = M' \sqcup - M''$, we can collar-glue them to obtain a bordism from $M$ to $M' …
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Gluing a manifold along its boundary, via chain complexes
I might have a idea how to prove my claim, that also generalizes to any stable $\infty$-category with duality functor:
Let $C$ be a chain complex, remember that there are natural diagonal and codiagon …
- 898