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Post Made Community Wiki by Ian Agol
The Kawauchi paper lemma 1.3 has a gap (the cap 2-handles C_i are not disjoint).
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edit approved Jun 13, 2018 at 17:42
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edit approved Jun 13, 2018 at 17:42
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Now Kawauchi claims that knotted surfaces in $S^4$ whose complement has cyclic fundamental group are smoothly trivial (i.e., bound a handlebody). See Corollary 1.3.

Note: This paper currently has a gap and the unknotting conjecture is not yet settled.

Now Kawauchi claims that knotted surfaces in $S^4$ whose complement has cyclic fundamental group are smoothly trivial (i.e., bound a handlebody). See Corollary 1.3.

Now Kawauchi claims that knotted surfaces in $S^4$ whose complement has cyclic fundamental group are smoothly trivial (i.e., bound a handlebody). See Corollary 1.3.

Note: This paper currently has a gap and the unknotting conjecture is not yet settled.

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Ian Agol
Ian Agol
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Now Kawauchi claims that knotted surfaces in $S^4$ whose complement has cyclic fundamental group are smoothly trivial (i.e., bound a handlebody). See Corollary 1.3.