Monday, 28 December 2015

gt.geometric topology - Is there a knotted torus in 4-sphere whose complement's fundamental group is 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?

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