Is there a knotted toritorus in 4-sphere whose complement's fundamental group is infinite cyclic ?

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edited May 9, 2010 at 15:07

Mariano Suárez-Álvarez

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Is there a knotted tori in 4-sphere with its complment'swhose complement's fundamental group is infinite cyclic ?

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asked May 9, 2010 at 14:42

Wolffo

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Is there a knotted tori in 4-sphere with its complment's fundamental group infinite cyclic ?

I am reading the book 'surface in 4-space' about the unknotting conjecture (Page 97): a 2-knot (2-sphere in 4-sphere) is trival if and only if the fundamental group of the exterior is infinite cyclic.

It said that in TOP category, Freedman proved the statement is true. I don't know why it is also true for general surface. in top category?

gt.geometric-topology

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Is there a knotted toritorus in 4-sphere whose complement's fundamental group is infinite cyclic ?

Is there a knotted tori in 4-sphere with its complment'swhose complement's fundamental group is infinite cyclic ?

Is there a knotted tori in 4-sphere with its complment's fundamental group infinite cyclic ?