Orbifolds And Stringy Topology
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Orbifolds and Stringy Topology
Author | : Alejandro Adem,Johann Leida,Yongbin Ruan |
Publsiher | : Cambridge University Press |
Total Pages | : 138 |
Release | : 2007-05-31 |
Genre | : Mathematics |
ISBN | : 9781139464482 |
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An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.
Compact Manifolds with Special Holonomy
Author | : Dominic D. Joyce |
Publsiher | : OUP Oxford |
Total Pages | : 460 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0198506015 |
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This is a combination of a graduate textbook on Reimannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It contains much new research and many new examples.
Global Homotopy Theory
Author | : Stefan Schwede |
Publsiher | : Cambridge University Press |
Total Pages | : 847 |
Release | : 2018-09-06 |
Genre | : Mathematics |
ISBN | : 9781108425810 |
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A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.
Algebraic Topology and Related Topics
Author | : Mahender Singh,Yongjin Song,Jie Wu |
Publsiher | : Springer |
Total Pages | : 313 |
Release | : 2019-02-02 |
Genre | : Mathematics |
ISBN | : 9789811357428 |
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This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.
Geometric and Topological Methods for Quantum Field Theory
Author | : Hernan Ocampo,Eddy Pariguan,Sylvie Paycha |
Publsiher | : Cambridge University Press |
Total Pages | : 435 |
Release | : 2010-04-29 |
Genre | : Science |
ISBN | : 9781139486736 |
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Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.
Women in Topology Collaborations in Homotopy Theory
Author | : Maria Basterra,Kristine Bauer,Kathryn Hess,Brenda Johnson |
Publsiher | : American Mathematical Soc. |
Total Pages | : 166 |
Release | : 2015-05-21 |
Genre | : Algebraic topology -- Applied homological algebra and category theory -- Abstract and axiomatic homotopy theory |
ISBN | : 9781470410131 |
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This volume contains the proceedings of the WIT: Women in Topology workshop, held from August 18-23, 2013, at the Banff International Research Station, Banff, Alberta, Canada. The Women in Topology workshop was devoted primarily to active collaboration by teams of five to seven participants, each including senior and junior researchers, as well as graduate students. This volume contains papers based on the results obtained by team projects in homotopy theory, including -infinity structures, equivariant homotopy theory, functor calculus, model categories, orbispaces, and topological Hochschild homology.
Strings and Geometry
Author | : Clay Mathematics Institute. Summer School,Isaac Newton Institute for Mathematical Sciences |
Publsiher | : American Mathematical Soc. |
Total Pages | : 396 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 082183715X |
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Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.
Geometry and Topology of Manifolds
Author | : Akito Futaki,Reiko Miyaoka,Zizhou Tang,Weiping Zhang |
Publsiher | : Springer |
Total Pages | : 348 |
Release | : 2016-06-03 |
Genre | : Mathematics |
ISBN | : 9784431560210 |
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Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists.The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, symplectic and contact geometry, and complex geometry.