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11	Superconnections and index theory Kahle, Alexander Rudolf 11 September 2012 (has links) This document presents a systematic investigation of the geometric index theory of Dirac operators coupled superconnections. A local version of the index theorem for Dirac operators coupled to superconnection is proved, and extended to families. An [eta]-invariant is defined, and it is shown to satisfy an APS-like theorem. A geometric determinant line bundle with section, metric, and connection is associated to a family of Dirac operators coupled to superconnections, and its holonomy is calculated in terms of the [eta]-invariant. / text Index theorems Vector bundles
12	Holomorphic vector bundles on compact Riemann surfaces 王朝輝, Wong, Chiu-fai. January 2000 (has links) published_or_final_version / Mathematics / Master / Master of Philosophy Vector bundles. Riemann surfaces.
13	The classification of ruled surfaces and rank 2 vector bundles over a curve of genus O or 1 / Malard, Joël. January 1983 (has links) No description available. Surfaces, Ruled. Vector bundles.
14	Superconnections and index theory Kahle, Alexander Rudolf. January 1900 (has links) Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references and index. Index theorems. Vector bundles.
15	On the infinitesimal isometries of fiber bundles / Konno, Tatsuo. January 2000 (has links) Univ., Diss.--Sendai, 2000. Fiber bundles (Mathematics)
16	Chern forms of positive vector bundles Guler, Dincer, January 2006 (has links) Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 44) Chern classes. Vector bundles.
17	Vector-valued Automorphic Forms and Vector Bundles Saber, Hicham January 2015 (has links) In this thesis we prove the existence of vector-valued automorphic forms for an arbitrary Fuchsian group and an arbitrary finite dimensional complex representation of this group. For small enough values of the weight as well as for large enough values, we provide explicit formulas for the spaces of these vector-valued automorphic forms (holomorphic and cuspidal). To achieve these results, we realize vector-valued automorphic forms as global sections of a certain family of holomorphic vector bundles on a certain Riemann surface associated to the Fuchsian group. The dimension formulas are then provided by the Riemann-Roch theorem. In the cases of 1 and 2-dimensional representations, we give some applications to the theories of generalized automorphic forms and equivariant functions. Automorphic Forms Vector Bundles
18	The moore spectral sequence for principal fibrations Donmez, Dogan January 1979 (has links) A proof of the Moore theorem which in the case of a principal fibration gives a spectral sequence converging to the homology of the base space is given. Also computed is the algebra structure of the homology of the Grassmannians, using Hopf algebra techniques and the cohomology of Grassmanians. Finally, it is shown that a spectral sequence for regular covering which was constructed earlier is a special case of the Moore Theorem. / Science, Faculty of / Mathematics, Department of / Graduate Fiber bundles (Mathematics)
19	The classification of ruled surfaces and rank 2 vector bundles over a curve of genus O or 1 / Malard, Joël. January 1983 (has links) No description available. Surfaces, Ruled. Vector bundles.
20	On a class of algebraic surfaces with numerically effective cotangent bundles Wang, Hongyuan, January 2006 (has links) Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 69-71).

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