# Questions tagged [surgery-theory]

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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### Fiber product formulae for surgery obstructions

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### Dehn surgery along primitive knot in 3-dimensional handlebody

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### Surgery for algebraic varieties

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### Are there alternate descriptions of `elementary cobordisms'?

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### Visualize how the 5d Dold manifold and Wu manifold are cobordant via a 6d manifolds with boundaries

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### Normal invariants

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### Bipartedly slice links and their surgeries

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### Concordance, surgery and homology cobordism

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### Dehn surgery on $S^3$ along a Hopf link with rational surgery coefficients

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### Integer surgeries along links yielding lens spaces

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### Torus trick without surgery theory

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### Negative surgeries on negative knots

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### Integer surgery on $S^3$

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### Confused about A. Kosinski's description about surgery in his book “differential manifolds”

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### Generalized Schoenflies - formalizing step in proof?

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### Rational surgery and attaching $2$-handles

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### Topological Spin manifolds in dimension 4

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### Realizing an amalgamated product of groups by splitting a closed manifold along a codimension 1 submanifold

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### Borromean Lines of three $\mathbb{R}^1$ in $\mathbb{R}^3$ and analogous Milnor link invariants

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### Diffeomorphism type of the added sphere in simply connected surgery

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### Wall self-intersection invariant for odd-dimensional manifolds?

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### What are these 3-manifolds from surgery?

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### Chirality and Anti-Chirality of links in 3 and in 5 dimensions

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### A user guide to the theory on Corks

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### Quartic link in a 5-sphere

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### Triple link in a 5-sphere — Proposal

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### Cell structures of simply-connected 5-manifolds (classified by Barden's 1965 paper)

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### Künneth formulas/theorem for bordism groups and cobordisms?

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### What is the monoid of skew-symmetric trilinear forms on finite abelian groups?

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### Regarding a proof in the surgery theorem by Gromov and Lawson

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### Surgery and Curvature on Foliation

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### A search for a sequence of $6$-manifolds

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### Making diffeomorphism of submanifolds boring

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### Building examples of elements of $\Omega_4(\xi)$ via surgery theory: how to do it?

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### Compare two topologies: Three 2-tori inside $S^3 \times S^1 \# S^2 \times S^2$ glued from two different diffeomorphisms

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### Vanishing of characteristic numbers vs vanishing of characteristic classes

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### What is the most symmetric configuration of four 2-surfaces linked in $S^4$?

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### A link of four 2-tori $T^2$ in $S^2 \times S^2$

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### A link of four 2-tori $T^2$ in $S^3 \times S^1 \# S^2 \times S^2 \# S^2 \times S^2$

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### Partial converse to Novikov's conjecture

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### Surgery on $M\times S^1$

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### How to compute $[CP^2, G/PL]$?

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### Manifolds whose diffeomorphism group has the homotopy type of a manifold itself

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### Classification of fake (quaternionic, octonionic) projective spaces

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### Does a homotopy sphere that bounds a highly connected manifold also bound a parallelizable manifold?

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### Elements of infinite order in the topological mapping class group

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### Surgery of $S^3$

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### Any PL-homology-manifold is homotopy equivalent to a manifold

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### Mapping class groups in high dimension

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