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arXiv · 2409.15693

Synthetic Homotopy Theory

Yuhang Wei
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Abstract

The goal of this dissertation is to present results from synthetic homotopy theory based on homotopy type theory (HoTT). After an introduction to Martin-L\"of's dependent type theory and homotopy type theory, key results include a synthetic construction of the Hopf fibration, a proof of the Blakers--Massey theorem, and a derivation of the Freudenthal suspension theorem, with calculations of some homotopy groups of $n$-spheres.

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Yuhang Wei. 2024-09-24. Synthetic Homotopy Theory. https://arxiv.org/abs/2409.15693

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