Immersions of surfaces

dc.contributor.advisorCo-chairs, Graduate Committee: David Ayala and Ryan Gradyen
dc.contributor.authorHoward, Adam Jacoben
dc.date.accessioned2022-06-10T18:58:50Z
dc.date.available2022-06-10T18:58:50Z
dc.date.issued2022en
dc.description.abstractTo determine the existence of a regular homotopy between two immersions, f, g : M --> N, is equivalent to showing that they lie in the same path component of the space Imm(M, N). We identify the connected components, pi 0 Imm(W g, M), of the space of immersions from a closed, orientable, genus-g surface W g into a parallelizable manifold M. We also identify the higher homotopy groups of Imm(W g, M) in terms of the homotopy groups of M and the Stiefel space V 2 (n). We then use this work to characterize immersions from tori into hyperbolic manifolds as self covers of a tubular neighborhood of a closed geodesic up to regular homotopy. Finally, we identify the homotopy-type of the space of framed immersions from the torus to itself.en
dc.identifier.urihttps://scholarworks.montana.edu/handle/1/16633en
dc.language.isoenen
dc.publisherMontana State University - Bozeman, College of Letters & Scienceen
dc.rights.holderCopyright 2022 by Adam Jacob Howarden
dc.subject.lcshManifolds (Mathematics)en
dc.subject.lcshHomotopy theoryen
dc.subject.lcshSurfacesen
dc.subject.lcshTorus (Geometry)en
dc.subject.lcshTopological spacesen
dc.titleImmersions of surfacesen
dc.typeDissertationen
mus.data.thumbpage35en
thesis.degree.committeemembersMembers, Graduate Committee: Jaroslaw Kwapisz; Lisa Davis; Lukas Geyeren
thesis.degree.departmentMathematical Sciences.en
thesis.degree.genreDissertationen
thesis.degree.namePhDen
thesis.format.extentfirstpage1en
thesis.format.extentlastpage146en

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