Grobner Bases And The Computation Of Group Cohomology
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Author | : David J. Green |
Publisher | : Springer Science & Business Media |
Total Pages | : 156 |
Release | : 2003-11-18 |
Genre | : Mathematics |
ISBN | : 9783540203391 |
Download Gröbner Bases and the Computation of Group Cohomology Book in PDF, Epub and Kindle
This monograph develops the Gröbner basis methods needed to perform efficient state of the art calculations in the cohomology of finite groups. Results obtained include the first counterexample to the conjecture that the ideal of essential classes squares to zero. The context is J. F. Carlson’s minimal resolutions approach to cohomology computations.
Author | : David J. Green |
Publisher | : |
Total Pages | : 156 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662191170 |
Download Grobner Bases and the Computation of Group Cohomology Book in PDF, Epub and Kindle
Author | : Graham Ellis |
Publisher | : Oxford University Press |
Total Pages | : 640 |
Release | : 2019-08-14 |
Genre | : Mathematics |
ISBN | : 0192569414 |
Download An Invitation to Computational Homotopy Book in PDF, Epub and Kindle
An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly illustrates how the basics of the subject can be implemented on a computer through its focus on fully-worked examples designed to develop problem solving techniques. The transition from basic theory to practical computation raises a range of non-trivial algorithmic issues which will appeal to readers already familiar with basic theory and who are interested in developing computational aspects. The book covers a subset of standard introductory material on fundamental groups, covering spaces, homology, cohomology and classifying spaces as well as some less standard material on crossed modules. These topics are covered in a way that hints at potential applications of topology in areas of computer science and engineering outside the usual territory of pure mathematics, and also in a way that demonstrates how computers can be used to perform explicit calculations within the domain of pure algebraic topology itself. The initial chapters include in-depth examples from data mining, biology and digital image analysis, while the later chapters cover a range of computational examples on the cohomology of classifying spaces that are likely beyond the reach of a purely paper-and-pen approach to the subject. An Invitation to Computational Homotopy serves as a self-contained and informal introduction to these topics and their implementation in the sphere of computer science. Written in a dynamic and engaging style, it skilfully showcases a range of useful machine computations, and will serve as an invaluable aid to graduate students working with algebraic topology.
Author | : Alejandro Adem |
Publisher | : Springer Science & Business Media |
Total Pages | : 333 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662062828 |
Download Cohomology of Finite Groups Book in PDF, Epub and Kindle
The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory. This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, and describes the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for computing the cohomology of important classes of groups including symmetric groups, alternating groups, finite groups of Lie type, and some of the sporadic simple groups, enable readers to acquire an in-depth understanding of group cohomology and its extensive applications.
Author | : William Wells Adams |
Publisher | : American Mathematical Soc. |
Total Pages | : 305 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 0821838040 |
Download An Introduction to Grobner Bases Book in PDF, Epub and Kindle
As the primary tool for doing explicit computations in polynomial rings in many variables, Gröbner bases are an important component of all computer algebra systems. They are also important in computational commutative algebra and algebraic geometry. This book provides a leisurely and fairly comprehensive introduction to Gröbner bases and their applications. Adams and Loustaunau cover the following topics: the theory and construction of Gröbner bases for polynomials with coefficients in a field, applications of Gröbner bases to computational problems involving rings of polynomials in many variables, a method for computing syzygy modules and Gröbner bases in modules, and the theory of Gröbner bases for polynomials with coefficients in rings. With over 120 worked examples and 200 exercises, this book is aimed at advanced undergraduate and graduate students. It would be suitable as a supplement to a course in commutative algebra or as a textbook for a course in computer algebra or computational commutative algebra. This book would also be appropriate for students of computer science and engineering who have some acquaintance with modern algebra.
Author | : Jon F. Carlson |
Publisher | : Springer Science & Business Media |
Total Pages | : 782 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 9401702152 |
Download Cohomology Rings of Finite Groups Book in PDF, Epub and Kindle
Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the first part was the computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64. The ideas and the programs for the calculations were developed over the last 10 years. Several new features were added over the course of that time. We had originally planned to include only a brief introduction to the calculations. However, we were persuaded to produce a more substantial text that would include in greater detail the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the com putations. We have gathered together many of the results and ideas that are the focus of the calculations from throughout the mathematical literature.
Author | : James Lepowsky |
Publisher | : Cambridge University Press |
Total Pages | : 415 |
Release | : 2010-06-03 |
Genre | : Mathematics |
ISBN | : 0521106648 |
Download Moonshine - The First Quarter Century and Beyond Book in PDF, Epub and Kindle
This volume examines the impact of the 'Monstrous Moonshine' paper on mathematics and theoretical physics.
Author | : Gianfranco Capriz |
Publisher | : Springer Science & Business Media |
Total Pages | : 228 |
Release | : 2008-04-18 |
Genre | : Technology & Engineering |
ISBN | : 3540782761 |
Download Mathematical Models of Granular Matter Book in PDF, Epub and Kindle
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.
Author | : Ana Carpio |
Publisher | : Springer Science & Business Media |
Total Pages | : 207 |
Release | : 2008-04-17 |
Genre | : Mathematics |
ISBN | : 3540785450 |
Download Inverse Problems and Imaging Book in PDF, Epub and Kindle
In the CIME Summer School on Imaging, experts in mathematical techniques and applications presented useful introductions to many aspects of the field. This volume contains updated lectures as well as additional contributions on other related topics.
Author | : Edward L. Green |
Publisher | : American Mathematical Soc. |
Total Pages | : 250 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821826794 |
Download Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering Book in PDF, Epub and Kindle
This volume presents the proceedings from the research conference, Symbolic Computation: Solving Equations in Algebra, Analysis, and Engineering, held at Mount Holyoke College, USA. It provides an overview of contemporary research in symbolic computation as it applies to the solution of polynomial systems. The conference brought together pure and applied mathematicians, computer scientists, and engineers, who use symbolic computation to solve systems of equations or who develop the theoretical background and tools needed for this purpose. Within this general framework, the conference focused on several themes: systems of polynomials, systems of differential equations, noncommutative systems, and applications.