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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/178613
Proof verification in algebraic topology
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Abstract
[en] Homotopy type theory is a relatively new field which results from the surprising blend of algebraic topology (homotopy) and type theory (type), that tries to serve as a theoretical base for theorem-proving software. This setting is particularly suitable for synthetic homotopy theory.
In this work, we describe how the programming language Agda can be used for proof verification, by examining the construction of the fundamental group of the circle $\mathbb{S}^{1}$. Then, trying to obtain the fundamental group of the real projective plane $\mathbb{R} \mathrm{P}^{2}$, we end up exploring a new construction of $\mathbb{R} \mathrm{P}^{2}$ as a higher inductive type.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Carles Casacuberta
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RIPOLL ECHEVESTE, Xavier. Proof verification in algebraic topology. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/178613