Isotopy in dimension 4

2 November 2020

The main result is the existence of smooth, properly embedded 3-discs in S¹ × D³ that are not smoothly isotopic to {1} × D³. We describe a 2-variable Laurent polynomial invariant of 3-discs in S¹ × D³. This allows us to show that, when taken up to isotopy, such 3-discs form an abelian group of infinite rank. Joint work with David Gabai.

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