A1 Algebraic Topology Over A Field PDF Download
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| Author | : Fabien Morel |
| Publisher | : Springer |
| Total Pages | : 267 |
| Release | : 2012-07-13 |
| Genre | : Mathematics |
| ISBN | : 3642295142 |
Download A1-Algebraic Topology over a Field Book in PDF, ePub and Kindle
This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.
| Author | : Mahender Singh |
| Publisher | : Springer |
| Total Pages | : 313 |
| Release | : 2019-02-02 |
| Genre | : Mathematics |
| ISBN | : 9811357420 |
Download Algebraic Topology and Related Topics Book in PDF, ePub and Kindle
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.
| Author | : Sergeĭ Vladimirovich Matveev |
| Publisher | : European Mathematical Society |
| Total Pages | : 112 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9783037190234 |
Download Lectures on Algebraic Topology Book in PDF, ePub and Kindle
Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.
| Author | : J. P. May |
| Publisher | : University of Chicago Press |
| Total Pages | : 262 |
| Release | : 1999-09 |
| Genre | : Mathematics |
| ISBN | : 9780226511832 |
Download A Concise Course in Algebraic Topology Book in PDF, ePub and Kindle
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
| Author | : Izzet Coskun |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 386 |
| Release | : 2017-07-12 |
| Genre | : Mathematics |
| ISBN | : 1470435578 |
Download Surveys on Recent Developments in Algebraic Geometry Book in PDF, ePub and Kindle
The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
| Author | : Skip Garibaldi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2010-07-16 |
| Genre | : Mathematics |
| ISBN | : 1441962115 |
Download Quadratic Forms, Linear Algebraic Groups, and Cohomology Book in PDF, ePub and Kindle
Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.
| Author | : Haynes Miller |
| Publisher | : CRC Press |
| Total Pages | : 982 |
| Release | : 2020-01-23 |
| Genre | : Mathematics |
| ISBN | : 1351251619 |
Download Handbook of Homotopy Theory Book in PDF, ePub and Kindle
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
| Author | : Frank Neumann |
| Publisher | : Springer Nature |
| Total Pages | : 223 |
| Release | : 2021-09-29 |
| Genre | : Mathematics |
| ISBN | : 3030789772 |
Download Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects Book in PDF, ePub and Kindle
This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on ‘Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects’ and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank’s contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.
| Author | : Mark E. Mahowald |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 366 |
| Release | : 1989 |
| Genre | : Mathematics |
| ISBN | : 0821851020 |
Download Algebraic Topology Book in PDF, ePub and Kindle
This book will provide readers with an overview of some of the major developments in current research in algebraic topology. Representing some of the leading researchers in the field, the book contains the proceedings of the International Conference on Algebraic Topology, held at Northwestern University in March, 1988. Several of the lectures at the conference were expository and will therefore appeal to topologists in a broad range of areas. The primary emphasis of the book is on homotopy theory and its applications. The topics covered include elliptic cohomology, stable and unstable homotopy theory, classifying spaces, and equivariant homotopy and cohomology. Geometric topics--such as knot theory, divisors and configurations on surfaces, foliations, and Siegel spaces--are also discussed. Researchers wishing to follow current trends in algebraic topology will find this book a valuable resource.
| Author | : Bjorn Ian Dundas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 228 |
| Release | : 2007-07-11 |
| Genre | : Mathematics |
| ISBN | : 3540458972 |
Download Motivic Homotopy Theory Book in PDF, ePub and Kindle
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
