![]() 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 |
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 = }}
All parameters are optional.
name
Strong multiplicity one theorem
, Zorn's lemma
. Defaults to page name.image
xxx.svg
.caption
type
Theorem
, Conjecture
, Lemma
, Postulate
, Axiom
.field of mathematics
Number theory
, Algebraic geometry and algebraic topology
.conjectured by
conjectured date
open problem
Yes
or No
, though something more specific could be put here (e.g. Only one example known
, etc.)first proof by
first proof date
implied by
generalizations
consequences
![]() 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 |
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 = }}
All parameters are optional.
name
Strong multiplicity one theorem
, Zorn's lemma
. Defaults to page name.image
xxx.svg
.caption
type
Theorem
, Conjecture
, Lemma
, Postulate
, Axiom
.field of mathematics
Number theory
, Algebraic geometry and algebraic topology
.conjectured by
conjectured date
open problem
Yes
or No
, though something more specific could be put here (e.g. Only one example known
, etc.)first proof by
first proof date
implied by
generalizations
consequences