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Counterexamples To Probl Me Des Topologies Of Grothendieck


Counterexamples To Probl Me Des Topologies Of Grothendieck
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Compactness And Contradiction


Compactness And Contradiction
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-03-22

Compactness And Contradiction written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-22 with Mathematics categories.


There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and nonrigorous to be discussed in the formal literature. Traditionally, it was a matter



Grothendieck Duality And Base Change


Grothendieck Duality And Base Change
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Author : Brian Conrad
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-12-12

Grothendieck Duality And Base Change written by Brian Conrad and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-12 with Mathematics categories.


Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.



The Topological Classification Of Stratified Spaces


The Topological Classification Of Stratified Spaces
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Author : Shmuel Weinberger
language : en
Publisher: University of Chicago Press
Release Date : 1994

The Topological Classification Of Stratified Spaces written by Shmuel Weinberger and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.


This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.



Foundations Of General Topology


Foundations Of General Topology
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Author : William J. Pervin
language : en
Publisher: Academic Press
Release Date : 2014-05-12

Foundations Of General Topology written by William J. Pervin and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.


Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction. This book provides a careful treatment of general topology. Organized into 11 chapters, this book begins with an overview of the important notions about cardinal and ordinal numbers. This text then presents the fundamentals of general topology in logical order processing from the most general case of a topological space to the restrictive case of a complete metric space. Other chapters consider a general method for completing a metric space that is applicable to the rationals and present the sufficient conditions for metrizability. This book discusses as well the study of spaces of real-valued continuous functions. The final chapter deals with uniform continuity of functions, which involves finding a distance that satisfies certain requirements for all points of the space simultaneously. This book is a valuable resource for students and research workers.



Topology And Geometry


Topology And Geometry
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Author : Glen E. Bredon
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-06-24

Topology And Geometry written by Glen E. Bredon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-24 with Education categories.


This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS



Algebraic Operads


Algebraic Operads
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Author : Jean-Louis Loday
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-08

Algebraic Operads written by Jean-Louis Loday and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-08 with Mathematics categories.


In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.



Quadratic Forms And Their Applications


Quadratic Forms And Their Applications
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Author : Eva Bayer-Fluckiger
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Quadratic Forms And Their Applications written by Eva Bayer-Fluckiger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.


This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.



Counterexamples To Probl Me Des Topologies Of Grothendieck


Counterexamples To Probl Me Des Topologies Of Grothendieck
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Author : Jari Taskinen
language : en
Publisher:
Release Date : 1986

Counterexamples To Probl Me Des Topologies Of Grothendieck written by Jari Taskinen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Linear topological spaces categories.