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gptkb:3-sphere_(S^3)
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H_2(S^3) = 0
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gptkb:S^1
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H_n = 0 for n > 1
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gptkb:7-dimensional_sphere
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H_0(S^7) = Z
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gptkb:quaternion_projective_plane
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Z in degrees 0, 4, 8
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gptkb:n-torus
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direct sum of binomial(n,k) copies of Z in degree k
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gptkb:15-sphere
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H_0(S^15) = Z
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gptkb:torus_T^n
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H_k(T^n) = (Z^{n \\choose k})
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gptkb:2-sphere_(S^2)
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H_2 = Z
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gptkb:standard_7-sphere
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H_k(S^7) = 0 for 0 < k < 7
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gptkb:7-dimensional_sphere
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H_k(S^7) = 0 for 0 < k < 7
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gptkb:standard_7-sphere
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H_7(S^7) = Z
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gptkb:n-torus_T^n
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H_k(T^n) = (Z^{n \\choose k})
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gptkb:7-dimensional_sphere
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H_7(S^7) = Z
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gptkb:2-sphere_(S^2)
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H_0 = Z
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gptkb:S^1
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H_1 = Z
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gptkb:15-sphere
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H_k(S^15) = 0 for 0 < k < 15
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gptkb:15-sphere
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H_15(S^15) = Z
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gptkb:sphere_S^{N-1}
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H_k(S^{N-1})
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gptkb:standard_7-sphere
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H_0(S^7) = Z
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gptkb:n-dimensional_torus
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direct sum of binomial(n,k) copies of Z in degree k
|