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gptkbp:instanceOf
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gptkb:topology
gptkb:Riemannian_manifold
|
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gptkbp:alsoKnownAs
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gptkb:2-torus
|
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gptkbp:can_be_constructed_as
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product of two circles
quotient of R^2 by Z^2
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|
gptkbp:dimensions
|
2
|
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gptkbp:embeddable_in
|
R^3
|
|
gptkbp:Euler_characteristic
|
0
|
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gptkbp:fundamentalGroup
|
Z × Z
|
|
gptkbp:genus
|
1
|
|
gptkbp:has_Betti_number_b_1
|
2
|
|
gptkbp:has_Betti_number_b_2
|
1
|
|
gptkbp:has_covering_space
|
R^2
|
|
gptkbp:homology_group_H_1
|
Z × Z
|
|
gptkbp:homology_group_H_2
|
Z
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
2-dimensional torus
|
|
gptkbp:includesMetric
|
flat metric
|
|
gptkbp:is_a_compact_space
|
true
|
|
gptkbp:is_a_complex_manifold
|
true
|
|
gptkbp:is_a_connected_space
|
true
|
|
gptkbp:is_a_fiber_bundle_over
|
gptkb:S^1
|
|
gptkbp:is_a_group_under_addition
|
true
|
|
gptkbp:is_a_Lie_group
|
true
|
|
gptkbp:is_a_parallelizable_manifold
|
true
|
|
gptkbp:is_a_smooth_manifold
|
true
|
|
gptkbp:is_a_surface_of_genus
|
1
|
|
gptkbp:is_a_surface_of_revolution
|
true
|
|
gptkbp:orientable
|
true
|
|
gptkbp:symbol
|
T^2
|
|
gptkbp:universalCover
|
R^2
|
|
gptkbp:bfsParent
|
gptkb:Flat_torus
gptkb:Loewner's_torus_inequality
|
|
gptkbp:bfsLayer
|
7
|