Milnor’s Construction of Exotic 7-spheres
نویسنده
چکیده
In this paper, I will provide a detailed explanation of Milnor’s construction of exotic 7-spheres. The candidate manifolds will be constructed as total spaces of S3 bundles over S4, denoted Mh,l. The subset of these candidates satisfying the condition h + l = ±1 will be shown to be topological spheres by Morse Theory. A subset of these that do not satisfy (h−l)2 ≡ 1 (mod 7) will be shown to not be differential spheres, by the Hirzebruch Signature Theorem and some other results from the theory of characteristic classes. Finally, I will discuss some interesting applications of exotic smooth structure throughout mathematics.
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تاریخ انتشار 2016