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 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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2023

Author dc:creator

• Kumanduri, Luis

Advisor dc:contributor.advisor

• Guth, Larry

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/151595

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/151595