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211	Non-Isotopic Symplectic Surfaces in Products of Riemann Surfaces Hays, Christopher January 2006 (has links) <html> <head> <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"> </head> Let Σ<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, for each <em>g</em> ≥ 1 and <em>h</em> ≥ 0 we construct an infinite set of infinite families of homotopic but pairwise non-isotopic symplectic surfaces inside the product symplectic manifold Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>. In particular, we achieve all positive genera from these families, providing first examples of infinite families of homotopic but pairwise non-isotopic symplectic surfaces of even genera inside Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>. Mathematics Symplectic Manifolds Isotopy Problem Branched Covers
212	Non-Isotopic Symplectic Surfaces in Products of Riemann Surfaces Hays, Christopher January 2006 (has links) <html> <head> <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"> </head> Let Σ<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, for each <em>g</em> ≥ 1 and <em>h</em> ≥ 0 we construct an infinite set of infinite families of homotopic but pairwise non-isotopic symplectic surfaces inside the product symplectic manifold Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>. In particular, we achieve all positive genera from these families, providing first examples of infinite families of homotopic but pairwise non-isotopic symplectic surfaces of even genera inside Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>. Mathematics Symplectic Manifolds Isotopy Problem Branched Covers
213	Deformations of functions and F-manifolds De Gregorio, Ignacio 10 December 2004 (has links) (PDF) In this thesis we study deformations of functions on singular varieties with a view toward Frobenius manifolds. <br /><br />Chapter 2 is mainly introductory. We prove standard results in deformation theory for which we do not know a suitable reference. We also give a construction of the miniversal deformation of a function on a singular space that to the best of our knowledge does not appear in this form in literature. <br /><br />In Chapter 3 we find a sufficient condition for the dimension of the base space of the miniversal deformation to be equal to the number of critical points into which the original singularity splits. We show that it holds for functions on smoothable and unobstructed curves and for function on isolated complete intersections singularities, unifying under the same argument previously known results. <br /><br />In Chapter 4 we use the previous results to construct a multiplicative structure known as F -manifold on the base space of the miniversal deformation. We relate our construction to the theory of Frobenius manifolds by means of an example: mirrors of weighted projective lines.<br /><br />The appendix is joint work with D. Mond. We study unfolding of composed functions under a suitable deformation category. It also yields an F-manifold structure on the base space, which we use to answer some questions raised by V. Goryunov and V. Zakalyukin on the discriminant on matrix deformations. [MATH] Mathematics Singularity Theory Frobenius manifolds
214	Learning on Riemannian manifolds for interpretation of visual environments Tuzel, Cuneyt Oncel. January 2008 (has links) Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Computer Science." Includes bibliographical references (p. 143-154).
215	The bigraded Rumin complex / Garfield, Peter McKee. January 2001 (has links) Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 120-124).
216	Essential surfaces in hyperbolic three-manifolds Leininger, Christopher Jay. January 2002 (has links) Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.
217	Orbifold euler characteristic of global quotients Hsia, Kwok-tung. January 2010 (has links) Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 68-70). Also available in print.
218	Approximate isometries and distortion energy functionals Bihun, Oksana, Chicone, Carmen Charles. January 2009 (has links) Title from PDF of title page (University of Missouri--Columbia, viewed on Feb. 11, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Professor Carmen Chicone. Vita. Includes bibliographical references.
219	On a Deodhar-type decomposition and a Poisson structure on double Bott-Samelson varieties Mouquin, Victor Fabien January 2013 (has links) Flag varieties of reductive Lie groups and their subvarieties play a central role in representation theory. In the early 1980s, V. Deodhar introduced a decomposition of the flag variety which was then used to study the Kazdan-Lusztig polynomials. A Deodhar-type decomposition of the product of the flag variety with itself, referred to as the double flag variety, was introduced in 2007 by B. Webster and M. Yakimov, and each piece of the decomposition was shown to be coisotropic with respect to a naturally defined Poisson structure on the double flag variety. The work of Webster and Yakimov was partially motivated by the theory of cluster algebras in which Poisson structures play an important role. The Deodhar decomposition of the flag variety is better understood in terms of a cell decomposition of Bott-Samelson varieties, which are resolutions of Schubert varieties inside the flag variety. In the thesis, double Bott-Samelson varieties were introduced and cell decompositions of a Bott-Samelson variety were constructed using shuffles. When the sequences of simple reflections defining the double Bott-Samelson variety are reduced, the Deodhar-type decomposition on the double flag variety defined by Webster and Yakimov was recovered. A naturally defined Poisson structure on the double Bott-Samelson variety was also studied in the thesis, and each cell in the cell decomposition was shown to be coisotropic. For the cells that are Poisson, coordinates on the cells were also constructed and were shown to be log-canonical for the Poisson structure. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy Schubert varieties Poisson manifolds Decomposition (Mathematics)
220	Monodromies of torsion D-branes on Calabi-Yau manifolds: extending the Douglas, et al., program Mahajan, Rahul Saumik 28 August 2008 (has links) Not available / text D-branes Monodromy groups Calabi-Yau manifolds

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