Desingularization: Invariants and Strategy: Application to Dimension 2, Cossart Vincent, Jannsen Uwe, Saito Shuji
Автор: Aroca, Jose M. Hironaka, Heisuke Vicente C Ordoba, Jos E Luis Название: Complex analytic desingularization ISBN: 4431702180 ISBN-13(EAN): 9784431702184 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
[From the foreword by B. Teissier] The main ideas of the proof of resolution of singularities of complex-analytic spaces presented here were developed by Heisuke Hironaka in the late 1960s and early 1970s. Since then, a number of proofs, all inspired by Hironaka's general approach, have appeared, the validity of some of them extending beyond the complex analytic case. The proof has now been so streamlined that, although it was seen 50 years ago as one of the most difficult proofs produced by mathematics, it can now be the subject of an advanced university course. Yet, far from being of historical interest only, this long-awaited book will be very rewarding for any mathematician interested in singularity theory. Rather than a proof of a canonical or algorithmic resolution of singularities, what is presented is in fact a masterly study of the infinitely near “worst” singular points of a complex analytic space obtained by successive “permissible” blowing ups and of the way to tame them using certain subspaces of the ambient space. This taming proves by an induction on the dimension that there exist finite sequences of permissible blowing ups at the end of which the worst infinitely near points have disappeared, and this is essentially enough to obtain resolution of singularities. Hironaka’s ideas for resolution of singularities appear here in a purified and geometric form, in part because of the need to overcome the globalization problems appearing in complex analytic geometry.
In addition, the book contains an elegant presentation of all the prerequisites of complex analytic geometry, including basic definitions and theorems needed to follow the development of ideas and proofs. Its epilogue presents the use of similar ideas in the resolution of singularities of complex analytic foliations. This text will be particularly useful and interesting for readers of the younger generation who wish to understand one of the most fundamental results in algebraic and analytic geometry and invent possible extensions and applications of the methods created to prove it.
Автор: David M. Jackson; Iain Moffatt Название: An Introduction to Quantum and Vassiliev Knot Invariants ISBN: 3030052125 ISBN-13(EAN): 9783030052126 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Нет в наличии. Описание: This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.
Автор: Prodan Emil, Schulz-Baldes Hermann Название: Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics ISBN: 3319805509 ISBN-13(EAN): 9783319805504 Издательство: Springer Рейтинг: Цена: 83850.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry.
Автор: Vladimir G. Turaev Название: Quantum Invariants of Knots and 3-Manifolds ISBN: 3110442663 ISBN-13(EAN): 9783110442663 Издательство: Walter de Gruyter Цена: 185890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents:Invariants of graphs in Euclidean 3-space and of closed 3-manifoldsFoundations of topological quantum field theoryThree-dimensional topological quantum field theoryTwo-dimensional modular functors6j-symbolsSimplicial state sums on 3-manifoldsShadows of manifolds and state sums on shadowsConstructions of modular categories
Автор: Dale Husem?ller; S. Echterhoff; B. Kr?tz; Michael Название: Basic Bundle Theory and K-Cohomology Invariants ISBN: 3540749551 ISBN-13(EAN): 9783540749554 Издательство: Springer Рейтинг: Цена: 74530.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object.
Автор: Monk J. Donald Название: Cardinal Invariants on Boolean Algebras ISBN: 3034807295 ISBN-13(EAN): 9783034807296 Издательство: Springer Рейтинг: Цена: 101550.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Along with almost 200 fascinating open problems, this updated edition covers most of what we know about Boolean cardinal invariants, and includes detailed studies of 21 cardinal number valued functions such as cellularity, defined for any Boolean algebra.
Автор: John D. Moore Название: Lectures on Seiberg-Witten Invariants ISBN: 3540412212 ISBN-13(EAN): 9783540412212 Издательство: Springer Рейтинг: Цена: 32560.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: An introduction to the theory of Seiberg-Witten invariants suitable for second-year graduate students. These invariants can be used to prove that there are many compact topological four-manifolds which have more than one smooth structure, and that others have no smooth structure at all.
Автор: Dale Husem?ller; S. Echterhoff; B. Kr?tz; Michael Название: Basic Bundle Theory and K-Cohomology Invariants ISBN: 3642094368 ISBN-13(EAN): 9783642094361 Издательство: Springer Рейтинг: Цена: 74530.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object.
Автор: Haruzo Hida Название: Elliptic Curves and Arithmetic Invariants ISBN: 1489990925 ISBN-13(EAN): 9781489990921 Издательство: Springer Рейтинг: Цена: 88500.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.
Автор: Hillman Jonathan Название: Algebraic Invariants Of Links (2Nd Edition) ISBN: 9814407380 ISBN-13(EAN): 9789814407380 Издательство: World Scientific Publishing Рейтинг: Цена: 126720.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. This second edition introduces two new chapters - twisted polynomial invariants and singularities of plane curves. Each replaces brief sketches in the first edition.
Автор: Smith, Larry Название: Polynomial Invariants of Finite Groups ISBN: 0367449137 ISBN-13(EAN): 9780367449131 Издательство: Taylor&Francis Рейтинг: Цена: 65320.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This is a book about the invariant theory of finite groups, written by an algebraic topologist. It illustrates the theorems by applying them to concrete cases, and examines several basic ideas and problems of invariant theory in the context of some elementary examples.
Автор: Roe Goodman; Nolan R. Wallach Название: Symmetry, Representations, and Invariants ISBN: 1441927298 ISBN-13(EAN): 9781441927293 Издательство: Springer Рейтинг: Цена: 55850.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book is a significant reworking of an earlier work by the authors. It offers a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that includes a broader range of applications.
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