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In the http://arxiv.org/abs/math/0606464v1 I read

"If you want to prove existence of exotic smooth structure on $\mathbb R^4$ you can do this if you are in possession of a knot which is topologically slice but not smoothly slice (slice means zero slice genus). Freedman has a result stating that a knot with Alexander polynomial 1 is topologically slice. We now have an obstruction (s being non-zero) to being smoothly slice." (p.28)

What does it meansmean? Does anyone know the construction of exotic $\mathbb R^4$ using slice knots? Please, give me a references, if there are several constructions.

Added: http://arxiv.org/abs/math/0408379. Does there exist some other construction?
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In the http://arxiv.org/pdf/math/0606464v1http://arxiv.org/abs/math/0606464v1 I read

"If you want to prove existence of exotic smooth structure on $\mathbb R^4$ you can do this if you are in possession of a knot which is topologically slice but not smoothly slice (slice means zero slice genus). Freedman has a result stating that a knot with Alexander polynomial 1 is topologically slice. We now have an obstruction (s being non-zero) to being smoothly slice." (p.28)

What does it means? Does anyone know the construction of exotic $\mathbb R^4$ using slice knots? Please, give me a references, if there are several constructions.

Added: http://arxiv.org/pdf/math/0408379http://arxiv.org/abs/math/0408379. Does there exist some other construction?
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In the http://arxiv.org/pdf/math/0606464v1 I read

"If you want to prove existence of exotic smooth structure on $\mathbb R^4$ you can do this if you are in possession of a knot which is topologically slice but not smoothly slice (slice means zero slice genus). Freedman has a result stating that a knot with Alexander polynomial 1 is topologically slice. We now have an obstruction (s being non-zero) to being smoothly slice." (p.28)

What does it means? Does anyone know the construction of exotic $\mathbb R^4$ using slice knots? Please, give me a references, if there are several constructions.

Added: http://arxiv.org/pdf/math/0408379. Does there exist some other construction?
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