TITLE: Is there a knotted torus in 4-sphere whose complement's fundamental group is infinite cyclic ?  
QUESTION [5 upvotes]: 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?

REPLY [3 votes]: Anthony Conway and Mark Powell give a proof that a locally flat embedded closed orientable surface in the 4-sphere whose complement has infinite cyclic fundamental group is topologically unknotted, provided that the genus is greater than or equal to 3 (the genus 0 case is a result of Freedman and Quinn as mentioned in the question).
Apart from Kawauchi's controversial work, the topological unknotting conjecture for genus 1 and 2 appears to be an open question.