|
gptkb:3-sphere_(S^3)
|
H_2(S^3) = 0
|
|
gptkb:torus_T^n
|
H_k(T^n) = (Z^{n \choose k})
|
|
gptkb:3-sphere_(S^3)
|
H_3(S^3) = Z
|
|
gptkb:15-sphere
|
H_k(S^15) = 0 for 0 < k < 15
|
|
gptkb:7-dimensional_sphere
|
H_0(S^7) = Z
|
|
gptkb:15-sphere
|
H_0(S^15) = Z
|
|
gptkb:standard_7-sphere
|
H_k(S^7) = 0 for 0 < k < 7
|
|
gptkb:2-sphere_(S^2)
|
H_0 = Z
|
|
gptkb:sphere_S^{N-1}
|
H_k(S^{N-1})
|
|
gptkb:R^n/Z^n
|
H_k(R^n/Z^n) = (Z choose n over k)
|
|
gptkb:2-sphere_(S^2)
|
H_1 = 0
|
|
gptkb:3-sphere_(S^3)
|
H_0(S^3) = Z
|
|
gptkb:n-torus
|
direct sum of binomial(n,k) copies of Z in degree k
|
|
gptkb:S^1
|
H_0 = Z
|
|
gptkb:n-torus_T^n
|
H_k(T^n) = (Z^{n \choose k})
|
|
gptkb:S^1
|
H_n = 0 for n > 1
|
|
gptkb:2-sphere_(S^2)
|
H_2 = Z
|
|
gptkb:15-sphere
|
H_15(S^15) = Z
|
|
gptkb:7-dimensional_sphere
|
H_k(S^7) = 0 for 0 < k < 7
|
|
gptkb:S^1
|
H_1 = Z
|