Homotopically nontrivial area contracting maps
Name
Kumanduri-Luis-phd-math-2023-thesis-pdf.pdf
Description
Thesis PDF
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851.31 KB
Format
Adobe PDF
Checksum (MD5)
4115a6712348176bc2fdc970af654983
Author(s)
Kumanduri, Luis
Advisor(s)
Guth, Larry
Date Issued
June 2023
Publisher
Massachusetts Institute of Technology
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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