I also have a long standing interest in rigorous foundations of conformal field theory and string theory, including algebraic approaches to conformal field theory. Equivariant stable homotopy theory with lewis, steinberger, and with contributions by mcclure a brief guide to some addenda and errata pdf american mathematical society memoirs and asterisque at ams. Introduction to equivariant cohomology in algebraic geometry dave anderson. Specifically with an eye towards equivariant differential topology such as pontryaginthom construction for equivariant cohomotopy. Topological ktheory, ktheory of c algebras, geometric and topological invarients, the functors k1 k2, k1, sk1 of orders and grouprings, higher algebraic ktheory, higher dimensional class groups of orders and group rings, higher ktheory of schemes, modm higher ktheory of exact categories, schemes. Equivariant cohomology in algebraic geometry 3 proposition 2. Introductory lectures on equivariant cohomology, paperback. It then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant. Equivariant homotopy and cohomology theory ebok j p. Can do all of algebraic topology of gspaces with gcategories a gposet partially ordered set is a gcategory with at most one morphism, denoted x y, between any two objects. Handbook of algebraic topology 1st edition elsevier.
The only point of such a basic, pointset topology textbook is to get you to the point where you can work through an algebraic topology text at the. Group actions on stacks and applications to equivariant string topology for stacks. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. Hamiltonian group actions and equivariant cohomology. Currently, i am most interested in motivic and equivariant homotopy theory, especially in equivariant constructions arising from real cobordism in both categories. Out motivation will be to provide a proof of the classical weyl character formula using a localization result. The book was published by cambridge university press in 2002 in both paperback and hardback editions, but only the paperback version is currently available isbn 0521795400. Equivariant ordinary homology and cohomology springerlink. Equivariant algebraic topology applied to some problems in topological combinatorics abstract. Equivariant homotopy and cohomology theory ams bookstore. Equivariant algebraic topology applied to some problems in. Discussion in the context of global equivariant homotopy theory is in. In a sense, the book could have been written thirty or forty years ago since virtually everything in it is at least that old. Equivariant cohomology is concerned with the algebraic topology of spaces with a.
Foundations of algebraic topology princeton university press. Equivariant homotopy and cohomology theory cbms regional. I have tried very hard to keep the price of the paperback. Around 1960, pierre conner conjectured that if a compact lie group g acts on a space x, then under certain finiteness conditions the vanishing of the cohomology of x implies the vanishing of the cohomology of the orbit space xg. Download free ebook of equivariant algebraic topology in pdf format or read online by soren illman published on 1972 by. Introduction to equivariant cohomology in algebraic geometry. What are some good references to learn the foundations of equivariant homotopy theory algebraic topology, for someone who has a background in basic homotopy theory and a tad more advanced algebraic topology. The book contains an introduction of symplectic vector spaces followed by symplectic manifolds and then hamiltonian group actions and the darboux theorem. Glimpses of equivariant algebraic topology department of. Algebraic topology also known as homotopy theory is a flourishing branch of modern mathematics. Equivariant ordinary homology and cohomology ebook, 2016.
For that reason, no algebraic topologist today would consider writing a book just about borel cohomology. Our primary reference is the book of chrissginzburg 1, chapters 5 and 6. Similarly powerful tools have been lacking, however, in the context of equivariant topology. Since algebraic topology is still developing rapidly any attempt to cover the whole subject would.
Download for offline reading, highlight, bookmark or take notes while you read handbook of algebraic topology. A localization theorem computes a global invariant in terms of local data, say at the zeros of a vector field or at the fixed points of the group action. A very helpful book ist bredons equivariant cohomology theories lecture notes, 1967. Distinguished lecture glimpses of equivariant algebraic topology. For some of the later chapters, it would be helpful to have some background on. It explains the main ideas behind some of the most striking recent advances in the subject. An alpine expedition through algebraic topology about this title. Unfortunately, there are no textbooks about bredon cohomology either as far as i know. He has also written many books in homotopy theory, which include a. What are classic papers in equivariant topology that every student should read. Truth be told, this is more of an advanced analysis book than a topology book, since that subject began with poincares analysis situs which introduced in a sense and dealt with the two functors.
Handbook of algebraic topology school of mathematics. Stefan waner filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. Bredon defines the equivariant cohomology in the same way as steenrod. The convexity theorem and toric manifolds give a comprehensive treatment of equivariant cohomology. The book begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the sullivan conjecture that. Bredon, and equivariant homotopy and cohomology theory by j. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of atiyahbott and berlinevergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a.
This springer book series publishes wellwritten monographs in pure and applied mathematics, aimed at researchers, postdocs, and advanced graduate students. The serre spectral sequence and serre class theory 237 9. This paper is a continuations of the project initiated in the book string topology for stacks. Free topology books download ebooks online textbooks. Equivariant ordinary homology and cohomology book, 2016. The book begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the sullivan conjecture that emphasizes its.
Cbms regional conference series in mathematics publication year 1996. This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. A course on differential topology is an essential prerequisite for this course. Raoul botts collected papers, books on differential geometry, equivariant cohomology i have just finished two projectsvol.
This book, published in 2002, is a beginning graduatelevel textbook on algebraic topology from a fairly classical point of view. Group actions on stacks and applications to equivariant. 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. The book begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the sullivan conjecture that emphasizes its relationship with classical smith theory. Purchase handbook of algebraic topology 1st edition. Equivariant ordinary homology and cohomology steven r. To get an idea you can look at the table of contents and the preface printed version.
To find out more or to download it in electronic form, follow this link to the download page. The viewpoint is quite classical in spirit, and stays well within the con. Equivariant homotopy and cohomology theory about this title. This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject.
April 30, 2011 abstract introduced by borel in the late 1950s, equivariant cohomology encodes information about how the topology of a space interacts with a group action. Can do all algebraic topology of gspaces with gposets. In this thesis we present several results on geometric combinatorics whose solution can be achieved by means of results and tools from algebraic topology. There is a progression, with the later portions of the book on the whole being more di cult than the earlier portions. We construct string operations on the so2 equivariant homology of the free loop. First defined in the 1950s, it has been introduced into ktheory and algebraic geometry, but. The goal of these lectures is to give an introduction to equivariant algebraic ktheory.
This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. In mathematics, equivariant topology is the study of topological spaces that possess certain symmetries. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. As examples of equivariant coarse homology theories we discuss equivariant coarse ordinary homology and equivariant coarse algebraic khomology. The students have all taken a basic course in algebraic topology they know homologycohomology and fundamental groups, but some may not know much more topology than that. Intersection theory in loop spaces, the cacti operad, string topology as field theory, a morse theoretic viewpoint, brane topology.
Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, in other words, with the symmetries of a space. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. Equivariant algebraic topology has developed in fits and starts ever. May, university of chicago, chicago, il, michael cole, gustavo r comezana, steven r costenoble, anthony d elmendorf, john p greenlees, l g lewis, robert j piacenza, georgia triantafillou and stefan waner.
Equivariant coarse homotopy theory and coarse algebraic k. String topology is the study of algebraic and differential topological properties of spaces of paths and loops in manifolds. In studying topological spaces, one often considers continuous maps. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. Most chapters end with problems that further explore and refine the concepts presented.
Download cv editorial responsibility development in mathematics, series editor. May university of chicago press, 1999 this book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics. Arthur wasserman, equivariant differential topology, topology vol. Moreover, we discuss the cone functor, its relation with equivariant homology theories in equivariant topology, and assembly and forgetcontrol maps.
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