 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 |
|---|---|
| Open problem | No |
| Field of mathematics | Geometric topology |
| Conjectured by | Henri Poincaré |
| Conjecture date | 1904 |
| First proof by | Grigori Perelman |
| First proof date | 2006 |
| Implied by | |
| Generalizations | Generalized Poincaré conjecture |
Usage edit
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 =
| open problem =
| field of mathematics =
| conjectured by =
| conjecture date =
| first proof by =
| first proof date =
| implied by =
| generalizations =
| consequences =
}}
Parameters edit
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 of mathematics- The branch(es) of mathematics to which the statement belong(s), e.g.
Number theory,Algebraic geometry and algebraic topology. conjectured by- Name of person(s) who first posed the statement.
conjectured date- Date(s) of when the statement was first posed.
open problem- Is this an open problem? Typical values are
YesorNo, though something more specific could be put here (e.g.Only one example known, etc.) first proof by- Name of person(s) who first proved the statement.
first proof date- Date(s) of when the statement was first proven.
implied by- Statement(s) that imply the current one.
generalizations- Statement(s) that generalize the current one.
consequences- Statement(s) that are implied by the current one.