Homotopically nontrivial area contracting maps
In this thesis, we investigate the existence of area contracting maps in a given ho-motopy class. In particular, we give various generalizations of Guth’s h-principle for k-dilation of maps between spheres to other manifolds. This includes all maps from highly connected domains and maps to highly co...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2023
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| Online Access: | https://hdl.handle.net/1721.1/151595 |
| Summary: | In this thesis, we investigate the existence of area contracting maps in a given ho-motopy class. In particular, we give various generalizations of Guth’s h-principle for k-dilation of maps between spheres to other manifolds. This includes all maps from highly connected domains and maps to highly connected targets with a homology vanishing condition. We give necessary and sufficient conditions for a homotopy class of maps 𝑋ᵐ → 𝑌ⁿ between closed oriented manifolds to have representatives with small 𝑘-dilation for 𝑘 = 𝑛, 𝑛 − 1 when 𝑘 > (𝑚 + 1)/2. |
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