Tag: Algebraic

Free Download Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry (798 Pages)
by Jean Gallier & Jocelyn Quaintance
English | 2022 | ISBN: 9811245029 | 799 pages | True PDF | 48.94 MB

Free Download Automorphisms of manifolds and algebraic K-theory: Part III By Michael S. Weiss, Bruce E. Williams
2014 | 122 Pages | ISBN: 147040981X | PDF | 1 MB
The structure space $\mathcal{S}(M)$ of a closed topological $m$-manifold $M$ classifies bundles whose fibers are closed $m$-manifolds equipped with a homotopy equivalence to $M$. The authors construct a highly connected map from $\mathcal{S}(M)$ to a concoction of algebraic $L$-theory and algebraic $K$-theory spaces associated with $M$. The construction refines the well-known surgery theoretic analysis of the block structure space of $M$ in terms of $L$-theory

Free Download Algebraic Function Fields and Codes by Henning Stichtenoth
English | PDF (True) | 2009 | 363 Pages | ISBN : 3540768777 | 5 MB
15 years after the ?rst printing of Algebraic Function Fields and Codes,the mathematics editors of Springer Verlag encouraged me to revise and extend the book. Besides numerous minor corrections and amendments, the second edition di?ers from the ?rst one in two respects. Firstly I have included a series of exercises at the end of each chapter. Some of these exercises are fairly easy and should help the reader to understand the basic concepts, others are more advanced and cover additional material. Secondly a new chapter titled "Asymptotic Bounds for the Number of Rational Places" has been added. This chapter contains a detailed presentation of the asymptotic theory of function ?elds over ?nite ?elds, including the explicit construction of some asymptotically good and optimal towers. Based on these towers, a complete and self-contained proof of the Tsfasman-Vladut-Zink Theorem is given. This theorem is perhaps the most beautiful application of function ?elds to coding theory. The codes which are constructed from algebraic function ?elds were ?rst introduced by V. D. Goppa. Accordingly I referred to them in the ?rst edition as geometric Goppa codes. Since this terminology has not generally been – cepted in the literature, I now use the more common term algebraic geometry codes or AG codes. I would like to thank Alp Bassa, Arnaldo Garcia, Cem Guneri, ¨ Sevan Harput and Alev Topuzo? glu for their help in preparing the second edition.

Free Download Mee Seong Im, "Algebraic and Topological Aspects of Representation Theory"
English | ISBN: 1470470349 | 2024 | 232 pages | PDF | 4 MB
This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20-21, 2021. Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in mathematical physics, representation theory, number theory, combinatorics, geometry, low-dimensional topology, and category theory. Papers in this volume contain original research, written by speakers and their collaborators. Many papers also discuss new concepts with detailed examples and current trends with novel and important results, all of which are invaluable contributions to the mathematics community.

Free Download Algebraic Cycles, Sheaves, Shtukas, and Moduli: Impanga Lecture Notes by Piotr Pragacz
English | PDF (True) | 2008 | 240 Pages | ISBN : 3764385367 | 2.1 MB
The articles in this volume are devoted to:

Free Download Ramified Surfaces: On Branch Curves and Algebraic Geometry in the 20th Century (Frontiers in the History of Science) by Michael Friedman
English | September 28, 2022 | ISBN: 3031057198 | 264 pages | MOBI | 6.82 Mb
The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon’s program of braid monodromy factorization.By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods.

Free Download POPULATION DYNAMICS: ALGEBRAIC AND PROBABILISTIC APPROACH by Utkir a Rozikov
English | May 6, 2020 | ISBN: 9811211221 | 460 pages | MOBI | 67 Mb
A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding. The main mathematical problem for a given population is to carefully examine the evolution (time dependent dynamics) of the population. The mathematical methods used in the study of this problem are based on probability theory, stochastic processes, dynamical systems, nonlinear differential and difference equations, and (non-)associative algebras.

Free Download Affine Algebraic Geometry : Geometry of Polynomial Rings (441 Pages)
by Masayoshi Miyanishi
English | 2024 | ISBN: 9811280088 | 441 pages | True PDF | 10.24 MB

Free Download Algebraic Topology: A Structural Introduction by Marco Grandis
English | December 29, 2021 | ISBN: 9811248354 | 372 pages | MOBI | 37 Mb
Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout – the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation. This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites – basic general topology and little else – and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions. It can be used as a textbook for a semester course or self-study, and a guidebook for further study.

Free Download Algebraic Surfaces in Positive Characteristics: Purely Inseparable Phenomena in Curves and Surfaces by Masayoshi Miyanishi, Hiroyuki Ito
English | August 4, 2020 | ISBN: 9811215200 | 456 pages | MOBI | 14 Mb
Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments.In the present book, we consider first the forms of the affine line or the additive group, classification of such forms and detailed analysis. The forms of the affine line considered over the function field of an algebraic curve define the algebraic surfaces with fibrations by curves with moving singularities. These fibrations are investigated via the Mordell-Weil groups, which are originally introduced for elliptic fibrations.This is the first book which explains the phenomena arising from purely inseparable coverings and Artin-Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces.Rational double points in positive characteristics are treated in detail with concrete computations. These kinds of computations are not found in current literature. Readers, by following the computations line after line, will not only understand the peculiar phenomena in positive characteristics, but also understand what are crucial in computations. This type of experience will lead the readers to find the unsolved problems by themselves.