Template:Infobox mathematical statement

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Poincaré conjecture

For compact 2-dimensional surfaces without boundary, if every loop can be continuously tightened to a point, then the surface is topologically homeomorphic to a 2-sphere (usually just called a sphere). The Poincaré conjecture, proved by Grigori Perelman, asserts that the same is true for 3-dimensional spaces.
Type	Theorem
Field	Geometric topology
Statement	Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
Conjectured by	Henri Poincaré
Conjectured in	1904
First proof by	Grigori Perelman
First proof in	2006
Implied by	Geometrization conjecture Thurston elliptization conjecture
Open problem	No
Generalizations	Generalized Poincaré conjecture

Usage

The Template:Infobox mathematical statement generates a right-hand side infobox, based on the specified parameters. To use this template, copy the following code in your article and fill in as appropriate:

{{Infobox mathematical statement
| name =
| image =
| caption =
| type =
| field =
| statement =
| conjectured by =
| conjecture date =
| first stated by =
| first stated in =
| first proof by =
| first proof date =
| open problem =
| known cases =
| implied by =
| equivalent to =
| generalizations =
| consequences =
}}

Parameters

All parameters are optional.

name

Name at the top of the infobox; should be the name of the statement, e.g. Strong multiplicity one theorem, Zorn's lemma. Defaults to page name.

image

Image, e.g. xxx.svg.

caption

Caption.

type

The current type of statement, e.g. Theorem, Conjecture, Lemma, Postulate, Axiom.

field

The branch(es) of mathematics to which the statement belong(s), e.g. Number theory, Algebraic geometry and algebraic topology.

statement

The mathematical statement.

conjectured by

Name of person(s) who first posed the statement.

conjectured date

Date(s) of when the statement was first posed.

first stated by

Name of person(s) who first posed the statement (alternative to using the word "conjectured").

first stated date

Date(s) of when the statement was first posed (alternative to using the word "conjectured").

first proof by

Name of person(s) who first proved the statement.

first proof date

Date(s) of when the statement was first proven.

open problem

Is this an open problem? Typical values are Yes or No, though something more specific could be put here (e.g. Only one example known, etc.)

known cases

The cases for which the statement is known (e.g. For all function fields or For all r > 3).

implied by

Statement(s) that imply the current one.

equivalent to

Statement(s) that both imply and are implied by the current one.

generalizations

Statement(s) that generalize the current one.

consequences

Statement(s) that are implied by the current one.

See also

• WP:Infobox

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