dc.rights.license | CC-BY-NC-ND | |
dc.contributor.advisor | Pino Gomez, A. del | |
dc.contributor.author | Haar, Floor ter | |
dc.date.accessioned | 2023-08-18T00:01:40Z | |
dc.date.available | 2023-08-18T00:01:40Z | |
dc.date.issued | 2023 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/44713 | |
dc.description.abstract | A smooth distribution is a smooth subbundle of the tangent bundle. Locally, smooth distributions are spanned by vector fields to which one can apply the Lie bracket. Intuitively, one can view a distribution as the ``allowed directions of motion’’, and the Lie bracket as a way of measuring whether at a point one can move in a direction by moving along the distribution. If we can move in any direction, we call a distribution bracket-generating. This thesis focusses on bracket-generating distributions called (2,3,5)-structures. These are maximally non-integrable 2-distributions on 5-manifolds.
The h-principle is a useful tool for classifying families of distributions up to homotopy. In 1969 Gromov proved a powerful result which shows that the h-principle holds for many types of (bracket-generating) distributions, on open manifolds. Therefore, a natural question to ask is, what about closed manifolds? In this thesis we define a special class of (2,3,5)-structures called overtwisted (2,3,5)-structures, and we prove that the h-principle holds for this family of distributions on closed manifolds. | |
dc.description.sponsorship | Utrecht University | |
dc.language.iso | EN | |
dc.subject | In this thesis we define overtwistedness in (2,3,5)-structures, and prove that the h-principle holds for these structures on closed manifolds. | |
dc.title | Overtwisted (2,3,5)-structures and the h-principle | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.keywords | differential topology; h-principle; (2,3,5)-structures; distributions; overtwistedness; contact structures; Engel structures | |
dc.subject.courseuu | Mathematical Sciences | |
dc.thesis.id | 22172 | |