Relation Between Abstract Homotopy and Geometric Homotopy
Title | Relation Between Abstract Homotopy and Geometric Homotopy PDF eBook |
Author | Sadanand Verma |
Publisher | |
Pages | 242 |
Release | 1959 |
Genre | Homotopy theory |
ISBN |
Abstract Homotopy And Simple Homotopy Theory
Title | Abstract Homotopy And Simple Homotopy Theory PDF eBook |
Author | K Heiner Kamps |
Publisher | World Scientific |
Pages | 476 |
Release | 1997-04-11 |
Genre | Mathematics |
ISBN | 9814502553 |
The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).
Relation Between Abstract Homotopy and Geometric Homotopy
Title | Relation Between Abstract Homotopy and Geometric Homotopy PDF eBook |
Author | Sadanand Verma |
Publisher | |
Pages | 0 |
Release | 1958 |
Genre | Homotopy theory |
ISBN |
Cech and Steenrod Homotopy Theories with Applications to Geometric Topology
Title | Cech and Steenrod Homotopy Theories with Applications to Geometric Topology PDF eBook |
Author | D. A. Edwards |
Publisher | Springer |
Pages | 303 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540381031 |
Etale Homotopy of Simplical Schemes
Title | Etale Homotopy of Simplical Schemes PDF eBook |
Author | Eric M. Friedlander |
Publisher | Princeton University Press |
Pages | 192 |
Release | 1982-12-21 |
Genre | Mathematics |
ISBN | 0691083177 |
This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry. Of particular interest are the discussions concerning the Adams Conjecture, K-theories of finite fields, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory, the author provides a new treatment of the foundations which is more general and more precise than previous versions. One purpose of this book is to offer the basic techniques and results of etale homotopy theory to topologists and algebraic geometers who may then apply the theory in their own work. With a view to such future applications, the author has introduced a number of new constructions (function complexes, relative homology and cohomology, generalized cohomology) which have immediately proved applicable to algebraic K-theory.
Homotopy Theory: An Introduction to Algebraic Topology
Title | Homotopy Theory: An Introduction to Algebraic Topology PDF eBook |
Author | |
Publisher | Academic Press |
Pages | 383 |
Release | 1975-11-12 |
Genre | Mathematics |
ISBN | 0080873804 |
Homotopy Theory: An Introduction to Algebraic Topology
Homotopy Theory via Algebraic Geometry and Group Representations
Title | Homotopy Theory via Algebraic Geometry and Group Representations PDF eBook |
Author | Mark E. Mahowald |
Publisher | American Mathematical Soc. |
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.