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Showing 1 to 20 of 55 for “"3-manifolds"”.
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Geometry of SU(3) Manifolds
<p>I study differential geometry of 6-manifolds endowed with various $SU(3)$ structures from three perspectives. The first is special Lagrangian geometry; The second is pseudo-Hermitian-Yang-Mills connections or more generally, $\omega$-anti-self dual instantons; The third is pseudo-holomorphic …
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Counting surfaces in 3-manifolds
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-08-01
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Knot complements and 3-manifolds
The study of 3-manifold groups has reached big success in the last few decades, with the proof of geometrization theorem by Perelman, and several virtually compact special theorems by Wise, etc. In this paper, we will explore several aspects of 3-manifold groups and see what it shows for the knot …
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Foliations For Quasi-Fuchsian 3-Manifolds
In this paper, we prove that if a quasi-Fuchsian 3-manifold contains a minimal surface whose principal curvatures are in (-1, 1), then it admits a foliation such that each leaf is a surface of constant mean curvature. The key method that we use here is volume preserving mean curvature flow.
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Spectral geometry of hyperbolic 3-manifolds
… involving geometric data of hyperbolic 3-manifolds. These give numerical relationships between quantities like volume, length of geodesics, area of embedded surfaces, isoperimetric constants, eigenvalues of the Laplacian, and Margulis numbers for hyperbolic 3-manifolds.
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Constructing Bitwisted Face Pairing 3-Manifolds
… for finding face pairing descriptions of 3-manifolds. In this paper, I will describe the construction in a way suitable for a more general audience than the original research papers. Along the way, I will describe Dehn Surgery and a set of moves which allows us to change the framings of a …
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On Small Geometric Invariants of 3-Manifolds
*This dissertation includes a CD that is compound (contains both a paper copy and a CD as part of the dissertation). The CD requires the following application: Windows 95/98.
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Characteristic Surfaces in Non-Orientable 3-Manifolds
Made available in DSpace on 2014-12-14T13:09:43Z (GMT). No. of bitstreams: 1 8009036.pdf: 2041200 bytes, checksum: 5d16581d000c71b8cea08e565d92afc1 (MD5) Previous issue date: 1979
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Ricci flow on 3-manifolds with symmetry
In this thesis, we proved that for a 3-manifold S2 x S1 with warped product metric, the isoperimetric ratio on the base manifold S2 has a low positive bound away from zero, if the scalar curvature on the 3-manifold is positive. We also obtained a monotonicity result under the condition that the …
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Min-max minimal surfaces in 3-manifolds
A Heegaard splitting of a 3-manifold gives rise to a natural set of sweepouts which by the Almgren-Pitts and Simon-Smith min-max theory generates a min-max sequence converging as varifolds to a smooth minimal surface (possibly disconnected, and with multiplicities). We prove a conjecture of …
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Gluing Z₂-Harmonic Spinors on 3-Manifolds
… of a gluing result for Z₂-harmonic spinors on 3-manifolds. Z₂-harmonic spinors are a singular version of classical harmonic spinors and naturally arise as limits of sequences of solutions to generalized SeibergWitten equations. The gluing problem studied here addresses the reverse question in the …
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Cycle-Free Twisted Face-Pairing 3-Manifolds
… rarely provide us with examples of 3-manifolds due to singularities that arise at the vertices. However, any face-pairing of a faceted 3-ball may be slighted modified so that its quotient is a genuine manifold, i.e. free of singularities. The modified face-pairing is called a twisted …
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Closed surfaces in knot complements and 3-manifolds
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms
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Decision Problems in the Fundamental Groups of 3-Manifolds
Made available in DSpace on 2014-12-14T13:09:33Z (GMT). No. of bitstreams: 1 7714944.pdf: 2075185 bytes, checksum: ab854052646961cd551e34a5ec6d423f (MD5) Previous issue date: 1977
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Transversely Holomorphic Flows on 3-Manifolds and Geodesible Vector Fields
… existence of transversely holomorphic flows on 3-manifolds; then an explicit form of the first Chern class of the normal bundle is given when the flow is Riemannian. We study the geodesibility of the projections of basic vector fields onto the normal bundle, in the regular and in the singular …
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Hyperbolic 3-manifolds of bounded volume and trace field degree
… In this paper, we conjecture the same for manifolds with more cusps, and give the first positive results in this direction. For example, in the 2-cusped case, if a manifold has linearly independent cusp shapes, we show that the manifold has the desired property. To prove the results, we use …
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Distribution of Holonomy about Closed Geodesics on Compact Hyperbolic 3-Manifolds
<p>An important feature of compact hyperbolic 3-manifolds is their closed geodesics, which have both geometric and dynamical implications. These geodesics are parametrized by their length and holonomy, which describes the angle of rotation by parallel transport about the geodesic. First, we prove …
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Heegaard splittings for an infinite family of closed orientable 3-manifolds
<p>Nothing in Chapter One is new. In Chapters Two and Four, the families of examples L<sub>i,j</sub>, M<sub>i,j</sub> and M<sub>i,j,k</sub> are new, although particular cases have been described in the literature; most notably L<sub>1,2</sub> and M<sub>1,2,3</sub> have been described by Barry …
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Higher-order polynomial invariants of 3-manifolds giving lower bounds for Thurston norm
… norm, d&d1;0 . To do this, we exhibit 3-manifolds whose Alexander norm is trivial but whose d&d1;n are strictly increasing and can be made arbitrarily large. Other applications are made to detecting 3-manifolds that fiber over S 1 and to detecting 4-manifolds that admit no symplectic …
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Realizations of simple Smale flows on three-manifolds
… discuss how to realize simple Smale flows on 3-manifolds. We use four-band and three-band templates to study the linking structure of two types of closed orbits known as attracting closed orbits and repelling closed orbits in the flow. This dissertation extends the work done by M. Sullivan on …
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