Synthetic Homotopy Theory
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912042512809984 |
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| author | Wei, Yuhang |
| author_facet | Wei, Yuhang |
| contents | The goal of this dissertation is to present results from synthetic homotopy theory based on homotopy type theory (HoTT). After an introduction to Martin-Löf'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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Synthetic Homotopy Theory Wei, Yuhang Algebraic Topology Logic 55U35, 55P99, 03B38 The goal of this dissertation is to present results from synthetic homotopy theory based on homotopy type theory (HoTT). After an introduction to Martin-Löf'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. |
| title | Synthetic Homotopy Theory |
| topic | Algebraic Topology Logic 55U35, 55P99, 03B38 |
| url | https://arxiv.org/abs/2409.15693 |