Download Free Elliptic Cohomology Book in PDF and EPUB Free Download. You can read online Elliptic Cohomology and write the review.

The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new.
A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.
The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
This volume records the lectures given at a conference to celebrate Professor Ioan James' 60th birthday.
The genesis of these notes was a series of four lectures given by the first author at the Tata Institute of Fundamental Research. It evolved into a joint project and contains many improvements and extensions on the material covered in the original lectures. Let $F$ be a finite extension of $q$, and $E$ an elliptic curve defined over $F$. The fundamental idea of the Iwasawa theory of elliptic curves, which grew out of Iwasawa's basic work on the ideal class groups of cyclotomic fields, is to study deep arithmetic questions about $E$ over $F$ via the study of coarser questions about the arithmetic of $E$ over various infinite extensions of $F$. At present, we only know how to formulate this Iwasawa theory when the infinite extension is a $p$-adic Lie extension for a fixed prime number $p$. These notes will mainly discuss the simplest non-trivial example of the Iwasawa theory of $E$ over the cyclotomic $zp$-extension of $F$. However, the authors also make some comments about the Iwasawa theory of $E$ over the field obtained by adjoining all $p$-power division points on $E$ to $F$. They discuss in detail a number of numerical examples, which illustrate the general theory beautifully. In addition, they outline some of the basic results in Galois cohomology which are used repeatedly in the study of the relevant Iwasawa modules. The only changes made to the original notes: The authors take modest account of the considerable progress which has been made in non-commutative Iwasawa theory in the intervening years. They also include a short section on the deep theorems of Kato on the cyclotomic Iwasawa theory of elliptic curves.
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Aims to give an exposition of generalized (co)homology theories that can be read by a group of mathematicians who are not experts in algebraic topology. This title starts with basic notions of homotopy theory, and introduces the axioms of generalized (co)homology theory. It also discusses various types of generalized cohomology theories.
This book will provide readers with an overview of some of the major developments in current research in algebraic topology. Representing some of the leading researchers in the field, the book contains the proceedings of the International Conference on Algebraic Topology, held at Northwestern University in March, 1988. Several of the lectures at the conference were expository and will therefore appeal to topologists in a broad range of areas. The primary emphasis of the book is on homotopy theory and its applications. The topics covered include elliptic cohomology, stable and unstable homotopy theory, classifying spaces, and equivariant homotopy and cohomology. Geometric topics--such as knot theory, divisors and configurations on surfaces, foliations, and Siegel spaces--are also discussed. Researchers wishing to follow current trends in algebraic topology will find this book a valuable resource.
The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.