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Scissors Congruences Group Homology Characteristic Classes
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Book Synopsis Scissors Congruences, Group Homology & Characteristic Classes by : Johan L Dupont
Download or read book Scissors Congruences, Group Homology & Characteristic Classes written by Johan L Dupont and published by World Scientific. This book was released on 2001-02-26 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of 1998. They provide an overview of the work of the author and the late Chih-Han Sah on various aspects of Hilbert's Third Problem: Are two Euclidean polyhedra with the same volume “scissors-congruent”, i.e. can they be subdivided into finitely many pairwise congruent pieces? The book starts from the classical solution of this problem by M Dehn. But generalization to higher dimensions and other geometries quickly leads to a great variety of mathematical topics, such as homology of groups, algebraic K-theory, characteristic classes for flat bundles, and invariants for hyperbolic manifolds. Some of the material, particularly in the chapters on projective configurations, is published here for the first time.
Book Synopsis Quandles and Topological Pairs by : Takefumi Nosaka
Download or read book Quandles and Topological Pairs written by Takefumi Nosaka and published by Springer. This book was released on 2017-11-20 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles.More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as “We shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandle”. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology.For applications in topology, it is shown that from the perspective that some existing results in topology can be recovered from some quandles, a method is provided to diagrammatically compute some “relative homology”. (Such classes since have been considered to be uncomputable and speculative). Furthermore, the book provides a perspective that unifies some previous studies of quandles.The former part of the book explains motivations for studying quandles and discusses basic properties of quandles. The latter focuses on low-dimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.
Book Synopsis Lectures on Functor Homology by : Vincent Franjou
Download or read book Lectures on Functor Homology written by Vincent Franjou and published by Birkhäuser. This book was released on 2015-12-08 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurélien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament’s theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko’s unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert’s fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin’s strict polynomial functors, a conceptual form of modules over the Schur algebra. Roman Mikhailov’s lectures highlight topological invariants: homoto py and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology. Lastly, Antoine Touzé’s introductory course on homological algebra makes the book accessible to graduate students new to the field. The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems.
Book Synopsis Groups, Combinatorics & Geometry by : A. A. Ivanov
Download or read book Groups, Combinatorics & Geometry written by A. A. Ivanov and published by World Scientific. This book was released on 2003 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book contains the proceedings of the L.M.S. Durham Symposium on Groups, Geometry and Combinatorics, July 16-26, 2001"--P. v.
Download or read book Etale Cohomology Theory written by Lei Fu and published by World Scientific. This book was released on 2011 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.
Book Synopsis Etale Cohomology Theory (Revised Edition) by : Lei Fu
Download or read book Etale Cohomology Theory (Revised Edition) written by Lei Fu and published by World Scientific. This book was released on 2015-02-27 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and ℓ-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.
Book Synopsis Introduction to the Theory of Valuations by : Semyon Alesker
Download or read book Introduction to the Theory of Valuations written by Semyon Alesker and published by American Mathematical Soc.. This book was released on 2018-06-27 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of valuations on convex sets is a classical part of convex geometry which goes back at least to the positive solution of the third Hilbert problem by M. Dehn in 1900. Since then the theory has undergone a multifaceted development. The author discusses some of Hadwiger's results on valuations on convex compact sets that are continuous in the Hausdorff metric. The book also discusses the Klain-Schneider theorem as well as the proof of McMullen's conjecture, which led subsequently to many further applications and advances in the theory. The last section gives an overview of more recent developments in the theory of translation-invariant continuous valuations, some of which turn out to be useful in integral geometry. This book grew out of lectures that were given in August 2015 at Kent State University in the framework of the NSF CBMS conference “Introduction to the Theory of Valuations on Convex Sets”. Only a basic background in general convexity is assumed.
Download or read book The Math You Need written by Thomas Mack and published by MIT Press. This book was released on 2023-10-31 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive survey of undergraduate mathematics, compressing four years of study into one robust overview. In The Math You Need, Thomas Mack provides a singular, comprehensive survey of undergraduate mathematics, compressing four years of math curricula into one volume. Without sacrificing rigor, this book provides a go-to resource for the essentials that any academic or professional needs. Each chapter is followed by numerous exercises to provide the reader an opportunity to practice what they learned. The Math You Need is distinguished in its use of the Bourbaki style—the gold standard for concision and an approach that mathematicians will find of particular interest. As ambitious as it is compact, this text embraces mathematical abstraction throughout, avoiding ad hoc computations in favor of general results. Covering nine areas—group theory, commutative algebra, linear algebra, topology, real analysis, complex analysis, number theory, probability, and statistics—this thorough and highly effective overview of the undergraduate curriculum will prove to be invaluable to students and instructors alike.
Book Synopsis Mathematical Omnibus by : D. B. Fuks
Download or read book Mathematical Omnibus written by D. B. Fuks and published by American Mathematical Soc.. This book was released on 2007 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.
Book Synopsis Inspired By S S Chern: A Memorial Volume In Honor Of A Great Mathematician by : Phillip A Griffiths
Download or read book Inspired By S S Chern: A Memorial Volume In Honor Of A Great Mathematician written by Phillip A Griffiths and published by World Scientific. This book was released on 2006-11-27 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shiing-Shen Chern (1911-2004) was one of the leading differential geometers of the twentieth century. In 1946, he founded the Mathematical Institute of Academia Sinica in Shanghai, which was later moved to Nanking. In 1981, he founded the Mathematical Sciences Research Institute (MSRI) at Berkeley and acted as the director until 1984. In 1985, he founded the Nankai Institute of Mathematics in Tianjin. He was awarded the National Medal of Science in 1975; the Wolf Prize in mathematics in 1984; and the Shaw Prize in mathematical sciences in 2004.Chern's works span all the classic fields of differential geometry: the Chern-Simons theory; the Chern-Weil theory, linking curvature invariants to characteristic classes; Chern classes; and other areas such as projective differential geometry and webs that are mathematically rich but currently have a lower profile. He also published work in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.Inspired by Chern and his work, former colleagues, students and friends — themselves highly regarded mathematicians in their own right — come together to honor and celebrate Chern's huge contributions. The volume, organized by Phillip Griffiths of the Institute for Advanced Study (Princeton), contains contributions by Michael Atiyah (University of Edinburgh), C-M Bai (Nankai), Robert Bryant (Duke University), Kung-Ching Chang (Peking University), Jeff Cheeger (New York University), Simon K Donaldson (Imperial College), Hélène Esnault (Universität Duisburg-Essen), Mo-Lin Ge (Nankai), Mark Green (University of California at Los Angeles), Phillip Griffiths (Institute for Advanced Study), F Reese Harvey (Rice University), Alain Hénaut (Université Bordeaux 1), Niky Kamran (McGill University), Bruce Kleiner (Yale), H Blaine Lawson, Jr (Suny at Stony Brook), Yiming Long (Nankai), Xiaonan Ma (UMR 7640 du CNRS), Luc Pirio (IRMAR, France), Graeme Segal (Oxford), Gang Tian (MIT), Jean-Marie Trepreau (Institut de Mathématiques de Jussieu), Jeff Viaclovsky (MIT), Wei Wang (Nankai), Wentsun Wu (Chinese Academy of Sciences), C N Yang (Tsinghua), Tan Zhang (Murray State University), Weiping Zhang (Nankai) and others.
Book Synopsis Topology And Physics - Proceedings Of The Nankai International Conference In Memory Of Xiao-song Lin by : Zhenghan Wang
Download or read book Topology And Physics - Proceedings Of The Nankai International Conference In Memory Of Xiao-song Lin written by Zhenghan Wang and published by World Scientific. This book was released on 2008-08-11 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.The volume includes works on picture (2+1)-TQFTs and their applications to quantum computing, Berry phase and Yang-Baxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, Gromov-Witten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flow, Calabi-Yau problems for CR manifolds, Milnor's conjecture on volume of simplexes, Heegaard genera of 3-manifolds, and the (A,B)-slice problem. It also includes five unpublished papers of Xiao-Song Lin and various speeches related to the memorial conference.
Book Synopsis Riemann-finsler Geometry by : Shiing-shen Chern
Download or read book Riemann-finsler Geometry written by Shiing-shen Chern and published by World Scientific Publishing Company. This book was released on 2005-05-10 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics. It has applications in many fields of the natural sciences. Curvature is the central concept in Riemann-Finsler geometry. This invaluable textbook presents detailed discussions on important curvatures such as the Cartan torsion, the S-curvature, the Landsberg curvature and the Riemann curvature. It also deals with Finsler metrics with special curvature or geodesic properties, such as projectively flat Finsler metrics, Berwald metrics, Finsler metrics of scalar flag curvature or isotropic S-curvature, etc. Instructive examples are given in abundance, for further description of some important geometric concepts. The text includes the most recent results, although many of the problems discussed are classical.
Book Synopsis Minimal Submanifolds And Related Topics by : Yuanlong Xin
Download or read book Minimal Submanifolds And Related Topics written by Yuanlong Xin and published by World Scientific. This book was released on 2003-12-15 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. This important book presents the Douglas-Rado solution to the Plateau problem, but the main emphasis is on the Bernstein problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and author's own contributions to Bernstein type theorems for higher codimension. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.
Book Synopsis The Index Theorem And The Heat Equation Method by : Yanlin Yu
Download or read book The Index Theorem And The Heat Equation Method written by Yanlin Yu and published by World Scientific. This book was released on 2001-07-02 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods.
Book Synopsis Differential Geometry And Physics - Proceedings Of The 23th International Conference Of Differential Geometric Methods In Theoretical Physics by : Weiping Zhang
Download or read book Differential Geometry And Physics - Proceedings Of The 23th International Conference Of Differential Geometric Methods In Theoretical Physics written by Weiping Zhang and published by World Scientific. This book was released on 2006-12-11 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.
Book Synopsis Contemporary Trends In Algebraic Geometry And Algebraic Topology by : Shiing-shen Chern
Download or read book Contemporary Trends In Algebraic Geometry And Algebraic Topology written by Shiing-shen Chern and published by World Scientific. This book was released on 2002-08-02 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics. It was devoted to memorializing those two outstanding and original Chinese mathematicians who had made significant contributions to algebraic geometry and algebraic topology, respectively. It also provided a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st Century mathematics. About 100 mathematicians participated in the conference, including Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, etc.This invaluable volume contains the selected papers presented at the conference. The topics include canonical maps of Gorenstein 3-folds, fundamental groups of algebraic curves, Chen's interated integrals, algebraic fiber spaces, and others.
Book Synopsis Iterated Integrals And Cycles On Algebraic Manifolds by : Bruno Harris
Download or read book Iterated Integrals And Cycles On Algebraic Manifolds written by Bruno Harris and published by World Scientific. This book was released on 2004-03-15 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This subject has been of great interest both to topologists and to number theorists. The first part of this book describes some of the work of Kuo-Tsai Chen on iterated integrals and the fundamental group of a manifold. The author attempts to make his exposition accessible to beginning graduate students. He then proceeds to apply Chen's constructions to algebraic geometry, showing how this leads to some results on algebraic cycles and the Abel-Jacobi homomorphism. Finally, he presents a more general point of view relating Chen's integrals to a generalization of the concept of linking numbers, and ends up with a new invariant of homology classes in a projective algebraic manifold. The book is based on a course given by the author at the Nankai Institute of Mathematics in the fall of 2001.
