Julio Sampietro's scientific contributions

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Publications (1)

Figure 1. Henri Poincaré.
Figure 2. René Thom.
Figure 3. John Milnor.
Figure 6. The manifold K h,l obtained by gluing an 8-disc along M h,l .
Figure 8. The manifold C := B1 ∪ −M2.

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The Exotic World of Milnor's Spheres
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January 2024

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Revista Colombiana de Matemáticas

Julio Sampietro

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Carlos Segovia

In his celebrated article of 1956, John Milnor established the existence of smooth structures on the 7-dimensional sphere that differs from the usual one. These so-called "exotic" structures have been of great interest ever since. The purpose of this article is to give a clear exposition of the different tools that Milnor used in order to provide an almost self-contained construction of exotic structures on the 7-dimensional sphere and then to show that they are not diffeomorphic to the standard sphere.

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