Torus trick

---

Robion Kirby's torus trick is a proof method employing an immersion of a punctured torus $\mathbb {T} ^{n}-\mathbb {D} ^{n}$ into $\mathbb {R} ^{n}$, where then smooth structures can be pulled back along the immersion and be lifted to covers. The torus trick is used in Kirby's proof. of the Annulus theorem in dimensions $n\geq 5$. It was also employed in further investigations of topological manifolds with Laurent C. Siebenmann

Applications of the torus trick

Here is a list of some further applications of the torus trick that appeared in the literature:

• Proving existence and uniqueness (up to isotopy) of smooth structures on surfaces
• Proving existence and uniqueness (up to isotopy) of PL structures on 3-manifolds

External links

• MathOverflow discussion on the Torus trick
• Video recording of interview with Robion Kirby
• Topological Manifolds Seminar (University of Bonn, 2021)

This article "Torus trick" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:Torus trick. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.

📰 Article(s) of the same category(ies)

• Combining dimensions
• Locally regular space

---