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Results tagged with surgery-theory
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user 8032
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.
3
votes
Accepted
Wall self-intersection invariant for odd-dimensional manifolds?
I doubt that what you are proposing as the receptacle for the obstruction is the correct abelian group. For one thing, you are not taking into account the involution on the canonical double cover of t …
- 18.5k
11
votes
topological type of smooth manifolds with prescribed homotopy type and pontryagin class
In the $1$-connected case, one may argue as follows:
Let $X$ be a closed $1$-connected smooth $n$-manifold, $n \ge 5$. The theory of the Spivak fibration shows that any homotopy equivalence $f: M^n …
- 18.5k