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dc.rights.licenseCC-BY-NC-ND
dc.contributor.advisorPino Gomez, A. del
dc.contributor.authorHaar, Floor ter
dc.date.accessioned2023-08-18T00:01:40Z
dc.date.available2023-08-18T00:01:40Z
dc.date.issued2023
dc.identifier.urihttps://studenttheses.uu.nl/handle/20.500.12932/44713
dc.description.abstractA 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.sponsorshipUtrecht University
dc.language.isoEN
dc.subjectIn this thesis we define overtwistedness in (2,3,5)-structures, and prove that the h-principle holds for these structures on closed manifolds.
dc.titleOvertwisted (2,3,5)-structures and the h-principle
dc.type.contentMaster Thesis
dc.rights.accessrightsOpen Access
dc.subject.keywordsdifferential topology; h-principle; (2,3,5)-structures; distributions; overtwistedness; contact structures; Engel structures
dc.subject.courseuuMathematical Sciences
dc.thesis.id22172


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