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Singularities of the Minimal Model Program
by Kollár, János    Kovács, Sándor   
(Hardcover - English - 9781107035348)
This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly d ..
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Lectures on Algebraic Cycles
by Bloch, Spencer       
(Hardcover - English - 9780521118422)
Spencer Bloch's 1979 Duke lectures, a milestone in modern mathematics, have been out of print almost since their first publication in 1980, yet they have remained influential and are still the best place to learn the guiding philosophy of algebraic cycles and motives. This edition, now professionally typeset, has a new preface by the author giving his perspective on developments in the field over the past 30 years. The theory of algebraic cycles encompasses such central problems in mathematics as the Hodge conjecture and the Bloch-Kato conjecture on special values of zeta functions. The book begins with Mumford's example showing that the Chow group of zero-cycle ..
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Higher Topos Theory (Am-170)
by Lurie, Jacob       
(Paperback - English - 9780691140490)
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory , Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-catego ..
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Algebraic Topology: A First Course
by Fulton, William       
(Paperback - English - 9780387943275)
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of ..
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Topology of Surfaces, Knots, and Manifolds
by Carlson, Stephan C.       
(Hardcover - English - 9780471355441)
Topology of Surfaces, Knots, and Manifolds offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links-the objects of interest in the appealing set of mathematical ideas known as "rubber sheet geometry." The result is a text that is accessible to a broad range of undergraduate students, yet still provides solid coverage of the mathematics underlying these topics. ..
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Intuitive Combinatorial Topology
by Stillwell, J.    Shenitzer, A.    Boltyanskii, V. G.
(Paperback - English - 9781441928825)
Topology is a relatively young and very important branch of mathematics which studies properties of objects which are preserved through deformations, twistings, and stretchings, but not tearing. This book is well suited as preparation for students who plan to take a course in algebraic topology but also for advanced undergraduates or beginning graduates to just find out what topology is all about. The book has more than 200 problems, plenty of examples, and over 200 illustrations. ..
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Thurston's Work on Surfaces (Mn-48)
by Fathi, Albert    Laudenbach, François    Poénaru, Valentin
(Paperback - English - 9780691147352)
This book provides a detailed exposition of William Thurston's work on surface homeomorphisms, available here for the first time in English. Based on material of Thurston presented at a seminar in Orsay from 1976 to 1977, it covers topics such as the space of measured foliations on a surface, the Thurston compactification of Teichm ller space, the Nielsen-Thurston classification of surface homeomorphisms, and dynamical properties of pseudo-Anosov diffeomorphisms. Thurston never published the complete proofs, so this text is the only resource for many aspects of the theory. Thurston was awarded the prestigious Fields Medal in 1982 as well as many other prizes an ..
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Topics in Topology. (Am-10), Volume 10
by Lefschetz, Solomon       
(Paperback - English - 9780691095738)
Solomon Lefschetz pioneered the field of topology--the study of the properties of many-sided figures and their ability to deform, twist, and stretch without changing their shape. According to Lefschetz, "If it's just turning the crank, it's algebra, but if it's got an idea in it, it's topology." The very word topology comes from the title of an earlier Lefschetz monograph published in 1920. In Topics in Topology Lefschetz developed a more in-depth introduction to the field, providing authoritative explanations of what would today be considered the basic tools of algebraic topology. Lefschetz moved to the United States from France in 1905 at the age of twenty- ..
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Rp. 1.709.000
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Topology Conference: Virginia Polytechnic Institute and State University, March 22 - 24, 1973
by Dickman, R. F.    Fletcher, P.   
(Paperback - English - 9783540066842)
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Linear Topological Spaces
by Kelley, J. L.    Namioka, I.   
(Hardcover - English - 9780387901695)
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Rp. 935.000
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Modern Geometry--Methods and Applications: Part III: Introduction to Homology Theory
by Burns, Robert G.    Dubrovin, B. a.    Fomenko, A. T.
(Hardcover - English - 9780387972718)
Over the past fifteen years, the geometrical and topological methods of the theory of manifolds have as- sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics. The three volumes of Modern Geometry - Methods and Applications contain a concrete exposition of these methods together with their main applications in mathematics and physics. This third volume, presented in highly accessible languages, concentrates in homology theory. It contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto. Both scientists and students of mathematics as well ..
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Invariant Manifolds
by Hirsch, M. W.    Pugh, C. C.    Shub, M.
(Paperback - English - 9783540081487)
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Rp. 1.019.000
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Introduction to Topological Manifolds
by Lee, John       
(Paperback - English - 9781461427902)
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded t ..
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Special Order
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Rp. 1.854.000
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Rp. 2.180.000
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Bousfield Classes and Ohkawa's Theorem: Nagoya, Japan, August 28-30, 2015
by Ohsawa, Takeo    Minami, Norihiko   
(Paperback - English - 9789811515903)
This volume originated in the workshop held at Nagoya University, August 28-30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: ul li Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? li li The fundamental theorem of Hopkins, Neeman, Thom ..
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A Gentle Introduction to Homological Mirror Symmetry
by Bocklandt, Raf       
(Hardcover - English - 9781108483506)
Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Partintroduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various ..
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A Gentle Introduction to Homological Mirror Symmetry
by Bocklandt, Raf       
(Paperback - English - 9781108728751)
Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Partintroduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various ..
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Singularities, Bifurcations and Catastrophes
by Montaldi, James       
(Hardcover - English - 9781107151642)
Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, exis ..
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Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem
by Hill, Michael A.    Hopkins, Michael J.    Ravenel, Douglas C.
(Hardcover - English - 9781108831444)
The long-standing Kervaire invariant problem in homotopy theory arose from geometric and differential topology in the 1960s and was quickly recognised as one of the most important problems in the field. In 2009 the authors of this book announced a solution to the problem, which was published to wide acclaim in a landmark Annals of Mathematics paper. The proof is long and involved, using many sophisticated tools of modern (equivariant) stable homotopy theory that are unfamiliar to non-experts. This book presents the proof together with a full development of all the background material to make it accessible to a graduate student with an elementary algebraic topolo ..
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The Math Student's Companion: For All Upper Primary School Aged Students
by Bevans, Wilkeisha S.       
(Paperback - English - 9781716638763)
The Bahamas' Ministry of Education describes mathematics as a formal discipline that exposes hidden patterns that help us understand our world. Now much more than arithmetic and geometry, mathematics is a diverse discipline that deals with technology, data, industry, measurements, and observations from science. There are mathematical models of natural phenomena, human behavior, and social systems. This booklet is designed specifically for students under the primary school system, both public and private. It's a study handbook that makes memorizing mathematics fun and easy-and covers basic skills in the primary school mathematics curriculum. Topics covered includ ..
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Rp. 425.000
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Handbook of Geometry and Topology of Singularities II
by Cisneros-Molina, José Luis    Lê, Dũng Tráng    Seade, José
(Hardcover - English - 9783030780234)
Preface.- Contents.- Chapter 1 The Analytic Classificatio of Irreducible Plane Curve Singularities.- Chapter 2 Plane algebraic curves with prescribed singularities.- Chapter 3 Limit of tangents on complex surfaces.- Chapter 4 Algebro-geometric equisingularity of Zariski.- Chapter 5 Intersection homology.- Chapter 6 Milnor's fibratio theorem for real and complex singularities.- Chapter 7 Lê Cycles and Numbers of hypersurface singularities.- Chapter 8 Introduction to mixed hypersurface singularity. - Chapter 9 From Singularities to Polyhedral Products.- Chapter 10 Complements to ample divisors and Singularities.- Index. ..
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