Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic K -Theory
| Author | : |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 507 |
| Release | : 2004 |
| Genre | : Homotopy theory |
| ISBN | : 9780821856819 |
Homotopy Theory Relations With Algebraic Geometry Group Cohomology And Algebraic K Theory
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Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory
| Author | : Paul Gregory Goerss |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 520 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821832859 |
As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.
Algebraic K-Theory
| Author | : Victor Percy Snaith |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 374 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821808184 |
The proceedings volume from the March 1996 conference is dedicated to the late Bob Thomason, one of the leading research mathematicians specializing in algebraic K-theory. Twelve contributions include research papers treated in the lectures at the conference, articles inspired by those lectures, an exposition of Thomason's famous result concerning the relationship between algebraic K-theory and etale cohomology, and an exposition explaining and elaborating upon unpublished work of O. Gabber on Bloch-Ogus-Gersten type resolutions in K-theory and algebraic geometry. Annotation copyrighted by Book News, Inc., Portland, OR
Homotopy Theory via Algebraic Geometry and Group Representations
| Author | : Mark E. Mahowald |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821808052 |
The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.
Algebraic Topology
| Author | : Jaume Aguade |
| Publisher | : Springer |
| Total Pages | : 339 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540467726 |
The papers in this collection, all fully refereed, original papers, reflect many aspects of recent significant advances in homotopy theory and group cohomology. From the Contents: A. Adem: On the geometry and cohomology of finite simple groups.- D.J. Benson: Resolutions and Poincar duality for finite groups.- C. Broto and S. Zarati: On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C. Ravenel: Morava K-theories of classifying spaces and generalized characters for finite groups.- K. Ishiguro: Classifying spaces of compact simple lie groups and p-tori.- A.T. Lundell: Concise tables of James numbers and some homotopyof classical Lie groups and associated homogeneous spaces.- J.R. Martino: Anexample of a stable splitting: the classifying space of the 4-dim unipotent group.- J.E. McClure, L. Smith: On the homotopy uniqueness of BU(2) at the prime 2.- G. Mislin: Cohomologically central elements and fusion in groups.
Higher Algebraic K-Theory: An Overview
| Author | : Emilio Lluis-Puebla |
| Publisher | : Springer |
| Total Pages | : 172 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540466398 |
This book is a general introduction to Higher Algebraic K-groups of rings and algebraic varieties, which were first defined by Quillen at the beginning of the 70's. These K-groups happen to be useful in many different fields, including topology, algebraic geometry, algebra and number theory. The goal of this volume is to provide graduate students, teachers and researchers with basic definitions, concepts and results, and to give a sampling of current directions of research. Written by five specialists of different parts of the subject, each set of lectures reflects the particular perspective ofits author. As such, this volume can serve as a primer (if not as a technical basic textbook) for mathematicians from many different fields of interest.
Interactions between Homotopy Theory and Algebra
| Author | : Luchezar L. Avramov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 352 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821838148 |
This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.
Algebraic K-Theory and Its Applications
| Author | : Jonathan Rosenberg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461243149 |
Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
Motivic Homotopy Theory
| Author | : Bjorn Ian Dundas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 228 |
| Release | : 2007-07-11 |
| Genre | : Mathematics |
| ISBN | : 3540458972 |
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Introduction to Homotopy Theory
| Author | : Paul Selick |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 220 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9780821844366 |
Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
