2026-09-20T08:04:06Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1515952023-08-01T03:24:19Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Guth, Larry
Kumanduri, Luis
Massachusetts Institute of Technology. Department of Mathematics
2023-07-31T19:51:17Z
2023-07-31T19:51:17Z
2023-06
2023-05-24T14:46:48.028Z
https://hdl.handle.net/1721.1/151595
In this thesis, we investigate the existence of area contracting maps in a given ho-motopy class. In particular, we give various generalizations of Guthβs 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 πα΅ β πβΏ between closed oriented manifolds to have representatives with small π-dilation for π = π, π β 1 when π > (π + 1)/2.
Ph.D.
Massachusetts Institute of Technology
In Copyright - Educational Use Permitted
Copyright retained by author(s)
https://rightsstatements.org/page/InC-EDU/1.0/
Homotopically nontrivial area contracting maps
Thesis
application/pdf
Doctoral
Doctor of Philosophy
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="b3a27713-9f3d-4f77-8c24-757f7cc35fad">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Title>Homotopically nontrivial area contracting maps</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2023-06</PublicationDate>
<Authors>
<Author>
<DisplayName>Kumanduri, Luis</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>https://rightsstatements.org/page/InC-EDU/1.0/</License>
<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 Guthβs 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 πα΅ β πβΏ between closed oriented manifolds to have representatives with small π-dilation for π = π, π β 1 when π > (π + 1)/2.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>