Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds
<p>The surface subgroup theorem, proved by Kahn and Markovic, states that the fundamental group of every closed hyperbolic 3-manifold contains a closed hyperbolic surface subgroup. The criterion of incompressibility, a criterion to ensure that an immersing surface to be essential, has played a...
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ndltd-CALTECH-oai-thesis.library.caltech.edu-102982021-10-29T05:01:32Z https://thesis.library.caltech.edu/10298/ Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds Fu, Lei <p>The surface subgroup theorem, proved by Kahn and Markovic, states that the fundamental group of every closed hyperbolic 3-manifold contains a closed hyperbolic surface subgroup. The criterion of incompressibility, a criterion to ensure that an immersing surface to be essential, has played an important role in their proof.</p> <p>In this thesis, we generalize the criterion of incompressibility from dimension three to all higher dimensions. Then we use the mixing property of the geodesic flow to construct a closed immersed surface which satisfies the assumption of our criterion when the hyperbolic manifold is in an odd dimension. Together, we prove the surface subgroup theorem in all odd dimensions.</p> 2017 Thesis NonPeerReviewed application/pdf en other https://thesis.library.caltech.edu/10298/1/Fu_Lei-main.pdf Fu, Lei (2017) Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9XK8CKN. https://resolver.caltech.edu/CaltechThesis:06062017-094601489 <https://resolver.caltech.edu/CaltechThesis:06062017-094601489> https://resolver.caltech.edu/CaltechThesis:06062017-094601489 CaltechThesis:06062017-094601489 10.7907/Z9XK8CKN |
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<p>The surface subgroup theorem, proved by Kahn and Markovic, states that the fundamental group of every closed hyperbolic 3-manifold contains a closed hyperbolic surface subgroup. The criterion of incompressibility, a criterion to ensure that an immersing surface to be essential, has played an important role in their proof.</p>
<p>In this thesis, we generalize the criterion of incompressibility from dimension three to all higher dimensions. Then we use the mixing property of the geodesic flow to construct a closed immersed surface which satisfies the assumption of our criterion when the hyperbolic manifold is in an odd dimension. Together, we prove the surface subgroup theorem in all odd dimensions.</p> |
author |
Fu, Lei |
spellingShingle |
Fu, Lei Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds |
author_facet |
Fu, Lei |
author_sort |
Fu, Lei |
title |
Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds |
title_short |
Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds |
title_full |
Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds |
title_fullStr |
Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds |
title_full_unstemmed |
Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds |
title_sort |
immersing essential surfaces in odd dimensional closed hyperbolic manifolds |
publishDate |
2017 |
url |
https://thesis.library.caltech.edu/10298/1/Fu_Lei-main.pdf Fu, Lei (2017) Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9XK8CKN. https://resolver.caltech.edu/CaltechThesis:06062017-094601489 <https://resolver.caltech.edu/CaltechThesis:06062017-094601489> |
work_keys_str_mv |
AT fulei immersingessentialsurfacesinodddimensionalclosedhyperbolicmanifolds |
_version_ |
1719491547340210176 |