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"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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"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?

3 edited tags; added 85 characters in body; added 2 characters in body

"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?

2 added 1 characters in body
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