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3-manifold and Geometric group theory

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

Difference between 3-manifold and Geometric group theory

3-manifold vs. Geometric group theory

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

Similarities between 3-manifold and Geometric group theory

3-manifold and Geometric group theory have 17 things in common (in Unionpedia): Abelian group, Annals of Mathematics, Dodecahedron, Finitely generated group, Geometrization conjecture, Group action, Homeomorphism, Hyperbolic geometry, Lie group, Low-dimensional topology, Mathematics, Mikhail Leonidovich Gromov, Mostow rigidity theorem, Pacific Journal of Mathematics, Presentation of a group, Topology, William Thurston.

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

3-manifold and Abelian group · Abelian group and Geometric group theory · See more »

Annals of Mathematics

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

3-manifold and Annals of Mathematics · Annals of Mathematics and Geometric group theory · See more »

Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

3-manifold and Dodecahedron · Dodecahedron and Geometric group theory · See more »

Finitely generated group

In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation) of finitely many elements of the finite set S and of inverses of such elements.

3-manifold and Finitely generated group · Finitely generated group and Geometric group theory · See more »

Geometrization conjecture

In mathematics, Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that can be associated with them.

3-manifold and Geometrization conjecture · Geometric group theory and Geometrization conjecture · See more »

Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

3-manifold and Group action · Geometric group theory and Group action · See more »

Homeomorphism

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

3-manifold and Homeomorphism · Geometric group theory and Homeomorphism · See more »

Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

3-manifold and Hyperbolic geometry · Geometric group theory and Hyperbolic geometry · See more »

Lie group

In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.

3-manifold and Lie group · Geometric group theory and Lie group · See more »

Low-dimensional topology

In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions.

3-manifold and Low-dimensional topology · Geometric group theory and Low-dimensional topology · See more »

Mathematics

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

3-manifold and Mathematics · Geometric group theory and Mathematics · See more »

Mikhail Leonidovich Gromov

Mikhail Leonidovich Gromov (also Mikhael Gromov, Michael Gromov or Mischa Gromov; Михаи́л Леони́дович Гро́мов; born 23 December 1943), is a French-Russian mathematician known for work in geometry, analysis and group theory.

3-manifold and Mikhail Leonidovich Gromov · Geometric group theory and Mikhail Leonidovich Gromov · See more »

Mostow rigidity theorem

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.

3-manifold and Mostow rigidity theorem · Geometric group theory and Mostow rigidity theorem · See more »

Pacific Journal of Mathematics

The Pacific Journal of Mathematics (ISSN 0030-8730) is a mathematics research journal supported by a number of American, Asian and Australian universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisation.

3-manifold and Pacific Journal of Mathematics · Geometric group theory and Pacific Journal of Mathematics · See more »

Presentation of a group

In mathematics, one method of defining a group is by a presentation.

3-manifold and Presentation of a group · Geometric group theory and Presentation of a group · See more »

Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

3-manifold and Topology · Geometric group theory and Topology · See more »

William Thurston

William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician.

3-manifold and William Thurston · Geometric group theory and William Thurston · See more »

The list above answers the following questions

3-manifold and Geometric group theory Comparison

3-manifold has 185 relations, while Geometric group theory has 130. As they have in common 17, the Jaccard index is 5.40% = 17 / (185 + 130).

References

This article shows the relationship between 3-manifold and Geometric group theory. To access each article from which the information was extracted, please visit:

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