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Lickorish–Wallace theorem

Index Lickorish–Wallace theorem

In mathematics, the Lickorish–Wallace theorem in the theory of 3-manifolds states that any closed, orientable, connected 3-manifold may be obtained by performing Dehn surgery on a framed link in the 3-sphere with ±1 surgery coefficients. [1]

15 relations: Andrew H. Wallace, Automorphism, Closed manifold, Dehn surgery, Dehn twist, Genus (mathematics), Knot (mathematics), Mathematics, Orientability, Simply connected space, Surface (topology), W. B. R. Lickorish, 3-manifold, 3-sphere, 4-manifold.

Andrew H. Wallace

Andrew Hugh Wallace (1926 – 18 January 2008) was a Scottish-American mathematician.

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Automorphism

In mathematics, an automorphism is an isomorphism from a mathematical object to itself.

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Closed manifold

In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary.

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Dehn surgery

In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a construction used to modify 3-manifolds.

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Dehn twist

In geometric topology, a branch of mathematics, a Dehn twist is a certain type of self-homeomorphism of a surface (two-dimensional manifold).

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Genus (mathematics)

In mathematics, genus (plural genera) has a few different, but closely related, meanings.

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Knot (mathematics)

In mathematics, a knot is an embedding of a circle S^1 in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Orientability

In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.

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Simply connected space

In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.

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Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

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W. B. R. Lickorish

William Bernard Raymond Lickorish (born 19 February 1938) is a mathematician.

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3-manifold

In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.

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3-sphere

In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.

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4-manifold

In mathematics, a 4-manifold is a 4-dimensional topological manifold.

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References

[1] https://en.wikipedia.org/wiki/Lickorish–Wallace_theorem

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