Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:topology surface |
| gptkbp:can_be_defined_as |
quotient of R^2 by Z^2
S^1 x S^1 |
| gptkbp:canBeEmbeddedIn |
R^3
|
| gptkbp:compact |
true
|
| gptkbp:connects |
true
|
| gptkbp:dimensions |
2
|
| gptkbp:Euler_characteristic |
0
|
| gptkbp:fundamentalGroup |
Z x Z
|
| gptkbp:genus |
1
|
| gptkbp:heldBy |
gptkb:Riemannian_manifold
gptkb:Lie_group Kähler manifold abelian group fiber bundle over S^1 with fiber S^1 |
| gptkbp:homology_group_H1 |
Z x Z
|
| gptkbp:homology_group_H2 |
Z
|
| https://www.w3.org/2000/01/rdf-schema#label |
2-torus
|
| gptkbp:orientable |
true
|
| gptkbp:symmetry |
GL(2,Z)
|
| gptkbp:universalCover |
R^2
|
| gptkbp:used_in |
gptkb:topology
gptkb:string_theory complex analysis differential geometry dynamical systems mathematical physics |
| gptkbp:bfsParent |
gptkb:U(1)_x_U(1)
|
| gptkbp:bfsLayer |
7
|