geometric topology contemporary mathematics

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Categorification In Geometry Topology And Physics

Author : Anna Beliakova
ISBN : 9781470428211
Genre : Categories (Mathematics)
File Size : 25. 61 MB
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The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.

Differential Geometry And Topology

Author : A.T. Fomenko
ISBN : 9780306109959
Genre : Mathematics
File Size : 33. 34 MB
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Combinatorial Methods In Topology And Algebraic Geometry

Author : John R. Harper
ISBN : 0821850393
Genre : Mathematics
File Size : 46. 80 MB
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This collection marks the recent resurgence of interest in combinatorial methods, resulting from their deep and diverse applications both in topology and algebraic geometry. Nearly thirty mathematicians met at the University of Rochester in 1982 to survey several of the areas where combinatorial methods are proving especially fruitful: topology and combinatorial group theory, knot theory, 3-manifolds, homotopy theory and infinite dimensional topology, and four manifolds and algebraic surfaces. This material is accessible to advanced graduate students with a general course in algebraic topology along with some work in combinatorial group theory and geometric topology, as well as to established mathematicians with interests in these areas.For both student and professional mathematicians, the book provides practical suggestions for research directions still to be explored, as well as the aesthetic pleasures of seeing the interplay between algebra and topology which is characteristic of this field. In several areas the book contains the first general exposition published on the subject. In topology, for example, the editors have included M. Cohen, W. Metzler and K. Sauerman's article on 'Collapses of $K\times I$ and group presentations' and Metzler's 'On the Andrews-Curtis-Conjecture and related problems'. In addition, J. M. Montesino has provided summary articles on both 3 and 4-manifolds.

Compact Riemann Surfaces

Author : Jürgen Jost
ISBN : 9783662047453
Genre : Mathematics
File Size : 31. 40 MB
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This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Geometry Topology And Mathematical Physics

Author : V. M. Buchstaber
ISBN : 0821836137
Genre : Mathematics
File Size : 83. 53 MB
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This volume contains a selection of papers based on presentations given at the S. P. Novikov seminar held at the Steklov Mathematical Institute in Moscow. Topics and speakers were chosen by the well-known expert, S. P. Novikov, one of the leading mathematicians of the twentieth century. His diverse interests are the tradition of the seminar and are reflected in the topics presented in the book. The book begins with Novikov's paper analyzing the position of mathematics and theoretical physics at the beginning of the new millennium. Following is an interview with Novikov published in the Newsletter of the European Mathematical Society presenting the genesis of many of his ideas and his scientific school. The remaining articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

Trends In Contemporary Mathematics

Author : Vincenzo Ancona
ISBN : 9783319052540
Genre : Mathematics
File Size : 51. 38 MB
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The topics faced in this book cover a large spectrum of current trends in mathematics, such as Shimura varieties and the Lang lands program, zonotopal combinatorics, non linear potential theory, variational methods in imaging, Riemann holonomy and algebraic geometry, mathematical problems arising in kinetic theory, Boltzmann systems, Pell's equations in polynomials, deformation theory in non commutative algebras. This work contains a selection of contributions written by international leading mathematicians who were speakers at the "INdAM Day", an initiative born in 2004 to present the most recent developments in contemporary mathematics.

Geometric Topology

Author : William Hilal Kazez
ISBN : 0821806548
Genre : Mathematics
File Size : 56. 88 MB
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This is Part 1 of a two-part volume reflecting the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. The texts include research and expository articles and problem sets. The conference covered a wide variety of topics in geometric topology. Features: Kirby's problem list, which contains a thorough description of the progress made on each of the problems and includes a very complete bibliography, makes the work useful for specialists and non-specialists who want to learn about the progress made in many areas of topology. This list may serve as a reference work for decades to come. Gabai's problem list, which focuses on foliations and laminations of 3-manifolds, collects for the first time in one paper definitions, results, and problems that may serve as a defining source in the subject area.

Geometric Topology

Author : Cameron Gordon
ISBN : 9780821851821
Genre : Mathematics
File Size : 75. 69 MB
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This volume contains the refereed proceedings of the conference.

Surveys In Contemporary Mathematics

Author : Nicholas Young
ISBN : 9780521705646
Genre : Mathematics
File Size : 46. 34 MB
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A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

Topics In Contemporary Mathematics

Author : Ignacio Bello
ISBN : 9781285528892
Genre : Mathematics
File Size : 53. 42 MB
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Written for the Math for Liberal Arts course, TOPICS IN CONTEMPORARY MATHEMATICS helps students see math at work in the world by presenting problem solving in purposeful and meaningful contexts. Many of the problems in the text demonstrate how math relates to subjects--such as sociology, psychology, business, and technology--that generally interest students. Available with InfoTrac Student Collections Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

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