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Topological invariants of contact structures and planar open booksArıkan, Mehmet Fırat. January 2008 (has links)
Thesis (Ph. D.)--Michigan State University. Dept. of Mathematics, 2008. / Title from PDF t.p. (viewed on July 23, 2009) Includes bibliographical references (p. 106-108). Also issued in print.
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Examples of hyperbolic knots with distance 3 toroidal surgeries in S³Garza, César, January 2009 (has links)
Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.
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Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds /Dunfield, Nathan M. January 1999 (has links)
Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 1999. / Includes bibliographical references. Also available on the Internet.
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Totally geodesic surfaces in hyperbolic 3-manifoldsDeBlois, Jason Charles, January 1900 (has links)
Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.
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On spin c-invariants of four-manifoldsLeung, Wai-Man Raymond January 1995 (has links)
The spin<sup>c</sup>-invariants for a compact smooth simply-connected oriented four-manifold, as defined by Pidstrigach and Tyurin, are studied in this thesis. Unlike the Donaldson polynomial invariants, they are defined by cutting down the moduli space M' of '1-instantons', which is the subspace of the moduli space M of anti-self-dual connections parametrizing coupled (spin<sup>c</sup>) Dirac operators with non-trivial kernel. Our main goal is to study the relationship between these spin<sup>c</sup>-invariants and the Donaldson polynomial invariants. The 'jumping subset' M' defined a cohomology class P of M which is given by the generalised Porteous formula. When the index l of the coupled Dirac operator is 1, the two smooth invariants are the same by definition. When l = 0 (or when M is compact), the spin<sup>c</sup>-invariants are expressable as a Donaldson polynomial evaluating the 'Porteous class' P. Our main results concern the first two non-trivial cases l = -1 and -2, when the generalised Porteous formula can not be applied directly. Using cut-and-paste arguments to the moduli space M, we show that for the former case the spin<sup>c</sup>-invariants and the contracted Donaldson invariants differ by a correction term. It is the number of points in the immediate lower stratum of the Uhlenbeck compactification times a universal 'linking invariant' on S<sup>4</sup>, which is obtained by computing an example (the K3 surface). The case when l = -2 and dimM = 8 is a parametrized version of the l = -1 situation and the correction term, which involves the same 'linking invariant', is obtained from a suitable obstruction theory.
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Heegaard Floer homology of certain 3-manifolds and cobordism invariantsDurusoy, Daniel Selahi. January 2008 (has links)
Thesis (Ph.D.)--Michigan State University. Mathematics, 2008. / Title from PDF t.p. (viewed on July 24, 2009) Includes bibliographical references (p. 40-41). Also issued in print.
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Lengths and homology of hyperbolic 3-manifolds /Masters, Joseph David, January 1999 (has links)
Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 67-69). Available also in a digital version from Dissertation Abstracts.
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Smooth finite cyclic group actions on positive definite four-manifolds /Tanase, Mihail. Hambleton, I. January 1900 (has links)
Thesis (Ph.D.)--McMaster University, 2003. / Advisor: Ian Hambleton. Includes bibliographical references (leaves 109-112). Also available via World Wide Web.
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Reconstructing and analyzing surfaces in 3-spaceSun, Jian, January 2007 (has links)
Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 129-135).
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Coherence for 3-dualizable objectsAraújo, Manuel January 2017 (has links)
A fully extended framed topological field theory with target in a symmetric monoidal n-catgeory C is a symmetric monoidal functor Z from Bord(n) to C, where Bord(n) is the symmetric monoidal n-category of n-framed bordisms. The cobordism hypothesis says that such field theories are classified by fully dualizable objects in C. Given a fully dualizable object X in C, we are interested in computing the values of the corresponding field theory on specific framed bordisms. This leads to the question of finding a presentation for Bord(n). In view of the cobordism hypothesis, this can be rephrased in terms of finding coherence data for fully dualizable objects in a symmetric monoidal n-category. We prove a characterization of full dualizability of an object X in terms of existence of a dual of X and existence of adjoints for a finite number of higher morphisms. This reduces the problem of finding coherence data for fully dualizable objects to that of finding coherence data for duals and adjoints. For n=3, and in the setting of strict symmetric monoidal 3-categories, we find this coherence data, and we prove the corresponding coherence theorems. The proofs rely on extensive use of a graphical calculus for strict monoidal 3-categories.
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