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Author : Michelle Previte
Publisher :
ISBN 13 :
Total Pages : 600 pages
Book Rating : 4.:/5 (484 download)
Download or read book The Topology of Four-dimensional Real Algebraic Sets written by Michelle Previte and published by . This book was released on 2000 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Selman Akbulut
Publisher : Springer Science & Business Media
ISBN 13 : 1461397391
Total Pages : 260 pages
Book Rating : 4.4/5 (613 download)
Download or read book Topology of Real Algebraic Sets written by Selman Akbulut and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Fall of 1975 we started a joint project with the ultimate goal of topo logically classifying real algebraic sets. This has been a long happy collaboration (c.f., [K2)). In 1985 while visiting M.S.R.1. we organized and presented our classification results up to that point in the M.S.R.1. preprint series [AK14] -[AK17]. Since these results are interdependent and require some prerequisites as well as familiarity with real algebraic geometry, we decided to make them self contained by presenting them as a part of a book in real algebraic geometry. Even though we have not arrived to our final goal yet we feel that it is time to introduce them in a self contained coherent version and demonstrate their use by giving some applications. Chapter I gives the overview of the classification program. Chapter II has all the necessary background for the rest of the book, which therefore can be used as a course in real algebraic geometry. It starts with the elementary properties of real algebraic sets and ends with the recent solution of the Nash Conjecture. Chapter III and Chapter IV develop the theory of resolution towers. Resolution towers are basic topologically defined objects generalizing the notion of manifold.
Author : Selman Akbulut
Publisher : American Mathematical Soc.
ISBN 13 : 0821802925
Total Pages : 170 pages
Book Rating : 4.8/5 (218 download)
Download or read book Real Algebraic Geometry and Topology written by Selman Akbulut and published by American Mathematical Soc.. This book was released on 1995 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Real Algebraic Geometry-Topology Conference, held at Michigan State University in December 1993. Presented here are recent results and discussions of new ideas pertaining to such topics as resolution theorems, algebraic structures, topology of nonsingular real algebraic sets, and the distribution of real algebraic sets in projective space.
Author : Saugata Basu
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871027
Total Pages : 238 pages
Book Rating : 4.8/5 (71 download)
Download or read book Algorithmic and Quantitative Real Algebraic Geometry written by Saugata Basu and published by American Mathematical Soc.. This book was released on 2003-01-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research. The articles are based on talks given at the DIMACS Workshop on ''Algorithmic and Quantitative Aspects of Real Algebraic Geometry''. Topics include deciding basic algebraic properties of real semi-algebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semi-algebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics. The book is intended for researchers interested in computational methods in algebra.
Author : Selman Akbulut
Publisher :
ISBN 13 :
Total Pages : 63 pages
Book Rating : 4.:/5 (218 download)
Download or read book The Topological Classification of 3-dimensional Real Algebraic Sets written by Selman Akbulut and published by . This book was released on 1985* with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael H. Freedman
Publisher : Princeton University Press
ISBN 13 : 1400861063
Total Pages : 268 pages
Book Rating : 4.4/5 (8 download)
Download or read book Topology of 4-Manifolds (PMS-39), Volume 39 written by Michael H. Freedman and published by Princeton University Press. This book was released on 2014-07-14 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of the International Congress of Mathematicians to Freedman in 1986. In Topology of 4-Manifolds these authors have collaborated to give a complete and accessible account of the current state of knowledge in this field. The basic material has been considerably simplified from the original publications, and should be accessible to most graduate students. The advanced material goes well beyond the literature; nearly one-third of the book is new. This work is indispensable for any topologist whose work includes four dimensions. It is a valuable reference for geometers and physicists who need an awareness of the topological side of the field. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Murray A. Marshall
Publisher : Springer
ISBN 13 : 3540699961
Total Pages : 191 pages
Book Rating : 4.5/5 (46 download)
Download or read book Spaces of Orderings and Abstract Real Spectra written by Murray A. Marshall and published by Springer. This book was released on 2006-11-17 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained as is the important application to minimal generation of semi-algebraic sets. Many results in the new theory of abstract real spectra (also called spaces of signs) appear here for the first time. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.
Author : Richard S. Palais
Publisher :
ISBN 13 :
Total Pages : 228 pages
Book Rating : 4.X/5 (1 download)
Download or read book Equivariant, Real Algebraic Differential Topology written by Richard S. Palais and published by . This book was released on 1972 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mccrory
Publisher : CRC Press
ISBN 13 : 9780824776213
Total Pages : 370 pages
Book Rating : 4.7/5 (762 download)
Download or read book Geometry and Topology written by Mccrory and published by CRC Press. This book was released on 1986-10-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.
Author : Saugata Basu
Publisher : Springer Science & Business Media
ISBN 13 : 3662053551
Total Pages : 602 pages
Book Rating : 4.6/5 (62 download)
Download or read book Algorithms in Real Algebraic Geometry written by Saugata Basu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
Author : José Seade
Publisher : Springer Science & Business Media
ISBN 13 : 3764373954
Total Pages : 243 pages
Book Rating : 4.7/5 (643 download)
Download or read book On the Topology of Isolated Singularities in Analytic Spaces written by José Seade and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an overview of selected topics on the topology of singularities, with emphasis on its relations to other branches of geometry and topology. This book studies real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations.
Author : D. S. Freed
Publisher : Springer Science & Business Media
ISBN 13 : 1468402587
Total Pages : 242 pages
Book Rating : 4.4/5 (684 download)
Download or read book Instantons and Four-Manifolds written by D. S. Freed and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the outcome of a seminar organized by Michael Freedman and Karen Uhlenbeck (the senior author) at the Mathematical Sciences Research Institute in Berkeley during its first few months of existence. Dan Freed (the junior author) was originally appointed as notetaker. The express purpose of the seminar was to go through a proof of Simon Donaldson's Theorem, which had been announced the previous spring. Donaldson proved the nonsmoothability of certain topological four-manifolds; a year earlier Freedman had constructed these manifolds as part of his solution to the four dimensional ; Poincare conjecture. The spectacular application of Donaldson's and Freedman's theorems to the existence of fake 1R4,s made headlines (insofar as mathematics ever makes headlines). Moreover, Donaldson proved his theorem in topology by studying the solution space of equations the Yang-Mills equations which come from ultra-modern physics. The philosophical implications are unavoidable: we mathematicians need physics! The seminar was initially very well attended. Unfortunately, we found after three months that we had covered most of the published material, but had made little real progress towards giving a complete, detailed proof. Mter joint work extending over three cities and 3000 miles, this book now provides such a proof. The seminar bogged down in the hard analysis (56 59), which also takes up most of Donaldson's paper (in less detail). As we proceeded it became clear to us that the techniques in partial differential equations used in the proof differ strikingly from the geometric and topological material.
Author : Frédéric Mangolte
Publisher : Springer Nature
ISBN 13 : 3030431045
Total Pages : 453 pages
Book Rating : 4.0/5 (34 download)
Download or read book Real Algebraic Varieties written by Frédéric Mangolte and published by Springer Nature. This book was released on 2020-09-21 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous.They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable. This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the “folklore”. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book. The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledge is presented, as well as major developments of the last twenty years in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem. Various levels of exercises are given, and the solutions of many of them are provided at the end of each chapter.
Author : Michel Coste
Publisher :
ISBN 13 :
Total Pages : 164 pages
Book Rating : 4.3/5 (91 download)
Download or read book Arc Spaces and Additive Invariants in Real Algebraic and Analytic Geometry written by Michel Coste and published by . This book was released on 2007 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume the authors present some new trends in real algebraic geometry based on the study of arc spaces and additive invariants of real algebraic sets. Generally, real algebraic geometry uses methods of its own that usually differ sharply from the more widely known methods of complex algebraic geometry. This feature is particularly apparent when studying the basic topological and geometric properties of real algebraic sets; the rich algebraic structures are usually hidden and cannot be recovered from the topology. The use of arc spaces and additive invariants partially obviates this disadvantage. Moreover, these methods are often parallel to the basic approaches of complex algebraic geometry. The authors' presentation contains the construction of local topological invariants of real algebraic sets by means of algebraically constructible functions. This technique is extended to the wider family of arc-symmetric semialgebraic sets. Moreover, the latter family defines a natural topology that fills a gap between the Zariski topology and the euclidean topology. In real equisingularity theory, Kuo's blow-analytic equivalence of real analytic function germs provides an equivalence relation that corresponds to topological equivalence in the complex analytic set-up. Among other applications, arc-symmetric geometry, via the motivic integration approach, gives new invariants of this equivalence, allowing some initial classification results. The volume contains two courses and two survey articles that are designed for a wide audience, in particular students and young researchers.
Author : Vladimir G. Turaev
Publisher : American Mathematical Soc.
ISBN 13 : 9780821827406
Total Pages : 300 pages
Book Rating : 4.8/5 (274 download)
Download or read book Topology, Ergodic Theory, Real Algebraic Geometry written by Vladimir G. Turaev and published by American Mathematical Soc.. This book was released on 2001 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of the Russian mathematician, V.A. Rokhlin (1919-1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmuller spaces, measure theory, etc. The book also includes a biography of Rokhlin by Vershik and two articles which should prove of historical interest.
Author : Vialar Thierry
Publisher : BoD - Books on Demand
ISBN 13 : 2955199052
Total Pages : 1134 pages
Book Rating : 4.9/5 (551 download)
Download or read book Handbook of Mathematics written by Vialar Thierry and published by BoD - Books on Demand. This book was released on 2023-08-22 with total page 1134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.
Author : Jacek Bochnak
Publisher : Springer Science & Business Media
ISBN 13 : 3662037181
Total Pages : 429 pages
Book Rating : 4.6/5 (62 download)
Download or read book Real Algebraic Geometry written by Jacek Bochnak and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is a translation, revision and updating of our book (pub lished in French) with the title "Geometrie Algebrique Reelle". Since its pub lication in 1987 the theory has made advances in several directions. There have also been new insights into material already in the French edition. Many of these advances and insights have been incorporated in this English version of the book, so that it may be viewed as being substantially different from the original. We wish to thank Michael Buchner for his careful reading of the text and for his linguistic corrections and stylistic improvements. The initial Jb. TEiX file was prepared by Thierry van Effelterre. The three authors participate in the European research network "Real Algebraic and Analytic Geometry". The first author was partially supported by NATO Collaborative Research Grant 960011. Jacek Bochnak April 1998 Michel Coste Marie-Pranroise Roy Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Ordered Fields, Real Closed Fields . . . . . . . . . . . . . . . . . . . . . . . 7 1. 1 Ordered Fields, Real Fields . . . . . " . . . . . . . . . . . . . . . . . . . . . . . 7 1. 2 Real Closed Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1. 3 Real Closure of an Ordered Field. . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 4 The Tarski-Seidenberg Principle. . . . . . . . . . . . . . . . . . . . . . . . . . 17 2. Semi-algebraic Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. 1 Algebraic and Semi-algebraic Sets. . . . . . . . . . . . . . . . . . . . . . . . 23 2. 2 Projection of Semi-algebraic Sets. Semi-algebraic Mappings. . 26 2. 3 Decomposition of Semi-algebraic Sets. . . . . . . . . . . . . . . . . . . . . 30 2. 4 Connectedness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2. 5 Closed and Bounded Semi-algebraic Sets. Curve-selection Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2. 6 Continuous Semi-algebraic Functions. Lojasiewicz's Inequality 42 2. 7 Separation of Closed Semi-algebraic Sets. . . . . . . . . . . . . . . . . .
