Sage thinks the unknot complement is simply-connected?

asked 2024-05-28 18:19:26 +0200

updated 2024-05-28 21:51:52 +0200

Max Alekseyev gravatar image

See title. When I run the following:

for K in KnotInfo:
    if K.num_components() == 1 and K.crossing_number() <= 5:
        print(K.name + ": " + str(K.link().fundamental_group()))

I get as output:

K0_1: Finitely presented group <  |  >
K3_1: Finitely presented group < x0, x1, x2 | x0*x2*x1^-1*x2^-1, x1*x0*x2^-1*x0^-1, x2*x1*x0^-1*x1^-1 >
K4_1: Finitely presented group < x0, x1, x2, x3 | x1*x0*x2^-1*x0^-1, x3*x2*x0^-1*x2^-1, x2*x1^-1*x3^-1*x1, x0*x3^-1*x1^-1*x3 >
K5_1: Finitely presented group < x0, x1, x2, x3, x4 | x1*x4*x2^-1*x4^-1, x2*x0*x3^-1*x0^-1, x3*x1*x4^-1*x1^-1, x4*x2*x0^-1*x2^-1, x0*x3*x1^-1*x3^-1 >
K5_2: Finitely presented group < x0, x1, x2, x3, x4 | x0*x2*x1^-1*x2^-1, x1*x4*x2^-1*x4^-1, x2*x0*x3^-1*x0^-1, x3*x1*x4^-1*x1^-1, x4*x3*x0^-1*x3^-1 >
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Comments

Can you please indicate the issue in the output? If you think there is an error, please report it at https://github.com/sagemath/sage/issues

Max Alekseyev gravatar imageMax Alekseyev ( 2024-05-29 18:16:32 +0200 )edit