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tfg_garcia_rivas_alejandro.pdf (748.39 KB)

Document type

Bachelor thesis

Publication date

2022-06-13

Publication license

cc-by-nc-nd (c) Alejandro García Rivas, 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/189742

Exotic smooths structures on spheres

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Abstract

[en] The main goal of this work is to prove the existence of exotic smooth spheres. These are smooth manifolds that are homeomorphic but not diffeomorphic to the standard sphere. This was first shown in the 7-dimensional case by John Milnor in his influential paper [Mil56], and this work replicates his construction. In order to state and prove this result, though, a journey through some background is needed. This includes singular homology and cohomology theory, Morse theory and characteristic classes. Hence, we also slightly develop these topics here.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Ricardo García López

Subject

Homologia, Treballs de fi de grau, Varietats topològiques, Topologia diferencial

Subject (English)

Homology, Bachelor's theses, Topological manifolds, Differential topology

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

GARCÍA RIVAS, Alejandro. Exotic smooths structures on spheres. [consulted: 8 of August of 2026]. Available at: https://hdl.handle.net/2445/189742

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