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Dehn's lemma

Index Dehn's lemma

In mathematics Dehn's lemma asserts that a piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disk's interior, implies the existence of another piecewise-linear map of the disk which is an embedding and is identical to the original on the boundary of the disk. [1]

16 relations: American Mathematical Society, Annals of Mathematics, Bulletin of the American Mathematical Society, Covering space, Disk (mathematics), Embedding, German Mathematical Society, Loop theorem, Mathematics, Mathematische Annalen, Piecewise linear function, Proceedings of the National Academy of Sciences of the United States of America, Sphere theorem (3-manifolds), Tower (mathematics), Yale University Press, 3-manifold.

American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Annals of Mathematics

The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.

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Bulletin of the American Mathematical Society

The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.

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Covering space

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.

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Disk (mathematics)

In geometry, a disk (also spelled disc).

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Embedding

In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.

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German Mathematical Society

The German Mathematical Society (Deutsche Mathematiker-Vereinigung – DMV) is the main professional society of German mathematicians.

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Loop theorem

In mathematics, in the topology of 3-manifolds, the loop theorem is a generalization of Dehn's lemma.

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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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Mathematische Annalen

Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.

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Piecewise linear function

In mathematics, a piecewise linear function is a real-valued function defined on the real numbers or a segment thereof, whose graph is composed of straight-line sections.

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Proceedings of the National Academy of Sciences of the United States of America

Proceedings of the National Academy of Sciences of the United States of America (PNAS) is the official scientific journal of the National Academy of Sciences, published since 1915.

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Sphere theorem (3-manifolds)

In mathematics, in the topology of 3-manifolds, the sphere theorem of gives conditions for elements of the second homotopy group of a 3-manifold to be represented by embedded spheres.

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Tower (mathematics)

In category theory, a branch of abstract mathematics, a tower is defined as follows.

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Yale University Press

Yale University Press is a university press associated with Yale University.

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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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Dehn lemma, Dehn's Lemma.

References

[1] https://en.wikipedia.org/wiki/Dehn's_lemma

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