Included is a discussion of postnikov towers and rational homotopy theory. Via the classical adjoint functors between the categories of commutative differential graded. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been read more. Books go search best sellers gift ideas new releases deals store coupons amazonbasics gift. Thomas and a great selection of related books, art and collectibles available now at. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the handbook. Rational homotopy theory is the study of spaces up to rational homotopy equivalence. Apart from the obvious attractiveness of learning a theory from its creator, it is written in an. Y is a map between rational spaces, then f is a rational homotopy equivalence if and only if f is a weak equivalence. This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups.
With its modern approach and timely revisions, this second edition of rational homotopy theory and differential forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory. It centers on the notion of calculability which is due to the author himself, as are the measuretheoretical and constructive points of view in rational homotopy. More recently, the closed model structure on the category of supplemented commutative graded algebras over a field was an important technical device in millers proof of sullivans conjecture on maps from classifying spaces to finite complexes 55. Morgan, rational homotopy theory and differential forms. This proceedings volume centers on new developments in rational homotopy and on their influence on algebra and algebraic topology. In part i we exhibit a chain of several categories connected by pairs of. Rational homotopy theory is the homotopy theory of rational topological spaces, hence of rational homotopy types. I am trying to read the paper rational homotopy theory by quillen and am stuck with the notion of complete augmented algebra. A quick introduction is also provided in the springer gtm by bott and tu. Homotopy of operads and grothendieckteichmuller groups.
We will use basic results from rational homotopy theory for which 7 has become a standard reference. This comprehensive monograph provides a selfcontained treatment of the theory of imeasure, or sullivans rational homotopy theory, from a constructive point of view. Rational homotopy theory and differential forms ebook by. The book produced by participants in the ias program was titled homotopy type theory. He had defined the complete augmented algebra and i dont understand. Rational homotopy theory and differential forms phillip. Q y, if their rationalizations x q and y q are homotopy equivalent. Then you can start reading kindle books on your smartphone, tablet, or computer. One can find many of these results in basic text books, such as may99, dol72.
Buy rational homotopy theory graduate texts in mathematics 2001 by yves felix, steve halperin, jeanclaude thomas isbn. Then you can start reading kindle books on your smartphone, tablet, or computer no kindle device required. The goal of rational homotopy theory is to understand this category. Consequently, this account will be valuable for nonspecialists and experts alike. It is based on a recently discovered connection between homotopy theory and type theory.
Rational homotopy theory and differential forms springerlink. This research monograph is a detailed account with complete proofs of rational homotopy theory for general nonsimply connected spaces, based on the minimal models introduced by sullivan in his original seminal article. Note that a weak equivalence is always a rational equivalence. There are even looser notions of equivalence, for example, two spaces are qequivalent if their rational homologies are equivalent. As the authors explain eloquently, the computational power of rational homotopy theory comes from its algebraic formulation, which was first discussed by sullivan and the mathematician daniel quillen, and involves the use of graded objects with both an algebraic structure and a differential. Rational homotopy theory by yves felix, 9781461265160, available at book depository with free delivery worldwide. The definition of the sullivan model for the rational homotopy of spaces is revisited, and the definition of models for. Rational homotopy theory ii, yves felix, steve halperin. The book by halperin, et al provides an overall survey of the area. Newest rationalhomotopytheory questions mathoverflow. As both notation and techniques of rational homotopy theory have been considerably simplified, the book presents modern elementary proofs for many results that were proven ten or fifteen years ago.
Despite the great progress made in only a few years, a textbook properly devoted to this subject still was lacking until now the appearance of the text in book form is highly welcome, since it will satisfy the need of many interested people. Rational homotopy theory and differential forms book. This monograph is a sequel to the book rational homotopy theory rht, published by springer in 2001, but is selfcontained except only that some results from rht are simply quoted without proof. The first part deals with foundations of equivariant stable homotopy theory. The underlying idea is that it should be possible to develop a purely algebraic approach to homotopy theory by.
This book consists of notes for a second year graduate course in advanced topology given by professor whitehead at m. This book is a second, augmented version of one of the famous books on rational homotopy. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Rational homotopy theory graduate texts in mathematics. Reprinted by university of chicago press, 1982 and 1992. Friedlander examines basic topology, emphasizing homotopy theory. Using the tools of homotopy theory, we can examine what kind of theory we get if we allow ourselves such a notion of equivalence.
Start with griffithsmorgans green book on rational homotopy. This monograph is a sequel to the book rational homotopy theory rht, published by springer in 2001, but is selfcontained except only that some results. This is a long awaited book on rational homotopy theory which contains all the main theorems with complete proofs, and more elementary proofs for many results that were proved ten or fifteen years ago. The theory of rational homotopy is the study of spaces with rational equivalences. In each case the rational homotopy type of a topological space is the same as the isomorphism class of its algebraic model and the rational homotopy type of a continuous map is the same as the algebraic homotopy class of the correspond ing morphism between models. Everyday low prices and free delivery on eligible orders. The computational power of rational homotopy theory is due to the discovery by. For further information on rationalization, the reader is refered to section 9 of 18. Rational homotopy theory 3 it is clear that for all r, sn r is a strong deformation retract of xr, which implies that hkxr 0 if k 6 0,n. Part of the graduate texts in mathematics book series gtm, volume 205. Rational homotopy theory by yves felix, stephen halperin. Basic definitions and constructions 494 kb contents. Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. He is known for being the prime architect of higher algebraic k theory, for which he was awarded the cole prize in 1975 and the fields medal in 1978.
Much of the theory is concerned with rationalization, the process that sends a general homotopy type to its closest rational approximation, in a. Rational homotopy theory is a subfield of algebraic topology. Rational homotopy theory ii and millions of other books are available for amazon kindle. Rational homotopy theory ii by steve halperin, 9789814651424, available at book depository with free delivery worldwide. Rational homotopy theory graduate texts in mathematics by yves felix, stephen halperin, j. Updated content throughout the book, reflecting advances in the area of homotopy theory. There are two seminal papers in the subject, quillens 20 and sullivans 25. Some of the early applications of the theory were in rational homotopy theory 4, 64. Furthermore, the homomorphism induced in reduced homology by the inclusion xr. Algebraic topology also known as homotopy theory is a flourishing branch of modern mathematics. Other readers will always be interested in your opinion of the books youve read.
The computational power of rational homotopy theory is due to the discovery by quillen 5 and by sullivan 144 of an explicit algebraic formulation. Rational homotopy theory and differential forms progress. The authors added a frist section on classical algebraic topology to make the book accessible to students with only little background in. Rational homotopy theory is the study of rational ho motopy types of spaces and of the properties of spaces and maps that are invariant under rational homotopy equivalence. In mathematics and specifically in topology, rational homotopy theory is a simplified version of. Rational homotopy theory ii world scientific publishing. Rational homotopy theory is today one of the major trends in algebraic topology. A list of recommended books in topology cornell university. Presupposing a knowledge of the fundamental group and of algebraic topology as far as singular theory, it is designed to introduce the student to some of the more important concepts of homotopy theory.
Enter your mobile number or email address below and well send you a link to download the free kindle app. What is the best way to study rational homotopy theory. Daniel gray dan quillen june 22, 1940 april 30, 2011 was an american mathematician from 1984 to 2006, he was the waynflete professor of pure mathematics at magdalen college, oxford. Rational homotopy theory and differential forms springer. Most of the papers are original research papers dealing with rational homotopy and tame homotopy, cyclic homology, moore conjectures on the exponents of the homotopy groups of a finite cwccomplex and homology of loop spaces. Rational homotopy theory is analogous to the study of linear algebra versus general ring. This monograph is a sequel to the book rational homotopy theory rht, published by springer in 2001, but is selfcontained. Also useful is the case of compact kahler manifolds treated in the paper by deligne, griffiths, morgan and sullivan in inventiones. Griffiths and morgan wrote a fine book on the subject. The topological intuition throughout the book, the recollections of the necessary elementary homotopy theory and the list of exercises make this book an excellent introduction to sullivans theory. In algebraic geometry and algebraic topology, branches of mathematics, a 1 homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. However, formatting rules can vary widely between applications and fields of interest or study. The theory is due to fabien morel and vladimir voevodsky.
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