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3-manifold and Mostow rigidity theorem

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between 3-manifold and Mostow rigidity theorem

3-manifold vs. Mostow rigidity theorem

In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, finite-volume hyperbolic manifold of dimension greater than two is determined by the fundamental group and hence unique.

Similarities between 3-manifold and Mostow rigidity theorem

3-manifold and Mostow rigidity theorem have 12 things in common (in Unionpedia): Annals of Mathematics, Closed manifold, Diffeomorphism, Fundamental group, Geometric group theory, Gromov norm, Homotopy, Hyperbolic space, Isomorphism, Mathematics, Teichmüller space, Volume form.

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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Closed manifold

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

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Diffeomorphism

In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.

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Fundamental group

In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

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Geometric group theory

Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).

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Gromov norm

In mathematics, the Gromov norm (or simplicial volume) of a compact oriented n-manifold is a norm on the homology (with real coefficients) given by minimizing the sum of the absolute values of the coefficients over all singular chains representing a cycle.

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Homotopy

In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.

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Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

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Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

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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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Teichmüller space

In mathematics, the Teichmüller space T(S) of a (real) topological (or differential) surface S, is a space that parametrizes complex structures on S up to the action of homeomorphisms that are isotopic to the identity homeomorphism.

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Volume form

In mathematics, a volume form on a differentiable manifold is a top-dimensional form (i.e., a differential form of top degree).

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The list above answers the following questions

3-manifold and Mostow rigidity theorem Comparison

3-manifold has 185 relations, while Mostow rigidity theorem has 29. As they have in common 12, the Jaccard index is 5.61% = 12 / (185 + 29).

References

This article shows the relationship between 3-manifold and Mostow rigidity theorem. To access each article from which the information was extracted, please visit:

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