Edwin henry spanier august 8, 1921 october 11, 1996 was an american mathematician at the university of california at berkeley, working in algebraic topology. This book provides an accessible introduction to algebraic topology, a. The first part covers the fundamental group, its definition and application in the study of covering spaces. However, imo you should have a working familiarity with euclidean geometry, college algebra, logic or discrete math, and set theory before attempting this book. Edwin henry spanier 1921 1996 article pdf available in notices of the american mathematical society 456 january 1998 with 1,016 reads how we measure reads. Springer graduate text in mathematics 9, springer, new york, 2010 r. Bredons sheaf theory, spaniers algebraic topology, or the original papers of steenrod and spanier prove continuity for cech cohomology on the category of compact hausdorff spaces. What are the best books on topology and algebraic topology. I would avoid munkres for algebraic topology, though. Aug 31, 2016 algebraic topology is, as the name suggests, a fusion of algebra and topology. Spanier now outdated or is it still advisable for a person with taste for category theory to study algebraic topology. The geometry of algebraic topology is so pretty, it would seem a pity to slight it and to miss all the intuition it provides. Spanier intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology.
It doesnt teach homology or cohomology theory,still you can find in it. This latter classification problem is of fundamental importance in algebraic topology, since it is the one where the tools available seem to be most successful. He coinvented spanierwhitehead duality and alexanderspanier cohomology, and wrote what was for a long time the standard textbook on algebraic topology spanier 1981. Mathematics cannot be done without actually doing it. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. An alternative use of the term is polyhedra polyhedral spaces in classical algebraic topology, e.
Algebraic topology math 414b, spring 2001, reading material. Algebraic topology math 414b, spring 2001, reading material the following is a list of books that you might like to refer to to supplement the lectures. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and simplicial complexes. As the title suggests, this short book is not designed to go into all the details but gives an introduction to the basic ideas. Algebraic topology ems european mathematical society. There are numerous classical books devoted to algebraic topology of which we mention three.
Algebraic topology is, as the name suggests, a fusion of algebra and topology. The main reason for taking up such a project is to have an electronic backup of my own handwritten solutions. Ross, abstract harmonic analysis nachbin, leopoldo, bulletin of the american mathematical society, 1967. The course is based on chapter 2 of allen hatchers book. Intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology. This book surveys the fundamental ideas of algebraic topology. A few of them will be available in the bookstore, and most will be on reserve in the library. A history of duality in algebraic topology james c. At the elementary level, algebraic topology separates naturally into the two broad. Im going to be controversial here, and suggest that you start with spanier s algebraic topology, supplemented by switzers algebraic topology. Bringing together researchers across the world to develop and use applied algebraic topology. From the answers to other questions on this site as well as mo, i learnt about the book algebraic.
Duality in the general course of human a airs seems to be a juxtaposition of complementary or opposite concepts. When i studied topology as a student, i thought it was abstract with no obvious applications to a field such as biology. The mathematics department dmath is responsible for mathematics instruction in all programs of study at the ethz. These are very good and comprehensive books which have stood the test of time. I have heard that spanier is a very nice book and meets the criterion of being categorical. Actually i think that in spirit it is more modern than many of the. 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. Spanier now outdated or is it still advisable for a person with taste for category theory to study algebraic topology from this book. A large number of students at chicago go into topology, algebraic and geometric. I think the treatment in spanier is a bit outdated.
Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Fundamentals of algebraic topology mathematical association of. Algebraic topology and the brain the intrepid mathematician. Free algebraic topology books download ebooks online. Spanier, quotients of contextfree languages kasher, asa, journal of symbolic logic, 1969.
A first course graduate texts in mathematics book online at best prices in india on. Basic algebraic topology and its applications mathematical. This frequently leads to poetical sounding uses of language, both in the common language and in the precision of mathematical. After reading the adams book, if you want to see some more serious applications of algebraic topology to knot theory, this book is a classic. Algebraic topology i and ii, reading material the following is a list of books that you might like to refer to to supplement the lectures. Building on rudimentary knowledge of real analysis, pointset topology, and basic algebra, basic algebraic topology provides plenty of material for a twosemester course in algebraic topology.
However, the going is difficult for those not initiated into the basic ideas. Introduction to algebraic topology by joseph rotman. This is a basic note in algebraic topology, it introduce the notion of fundamental groups, covering spaces, methods for computing fundamental groups using seifert van kampen theorem and some applications such as the brouwers fixed point theorem, borsuk ulam theorem, fundamental theorem of algebra. But it looks to be very old and i am afraid it could be outdated.
A weaker equivalence relation, based on continuous deformation, leads to another classification problem. The reader of this book is assumed to have a grasp of the elementary. I have tried very hard to keep the price of the paperback. For students concentrating in mathematics, the department offers a rich and carefully coordinated program of courses and seminars in a broad range of fields of pure and applied mathematics. An intuitive approach, translations of mathematical monographs volume 183, ams, 1996. Teubner, stuttgart, 1994 the current version of these notes can be found under. Oct 29, 2009 the more and more algebraic topology that i learn the more i continue to come back to hatcher for motivation and examples. This book is worth its weight in gold just for all the examples both throughout the text and in the exercises. Free algebraic topology books download ebooks online textbooks. Theres a great book called lecture notes in algebraic topology by davis and kirk which i highly recommend for advanced beginners, especially those who like the categorical viewpoint and homological algebra. This note provides an introduction to algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory. Be part of this community and help us grow this network.
This book is written as a textbook on algebraic topology. This is an ongoing solutions manual for introduction to algebraic topology by joseph rotman 1. Welcome to the applied algebraic topology research network. Basic algebraic topology and its applications download. While algebraic topology lies in the realm of pure mathematics, it is now finding applications in the real world. Undoubtedly, the best reference on topology is topology by munkres. It is not mandatory to hand in the exercises there is no testat. The exercise sheets can be handed in in the post box of felix hensel located in hg f 28. Adhikari closes his opus with material having to do with more relations between homology and homotopy hurewicz and more. If you dont, kosniowski has a nice treatment of pointset topology in first 14 of his book that is just enough to learn algebraic topology in either kosniowski or massey. Other readers will always be interested in your opinion of the books youve read.
Special pages permanent link page information wikidata item cite this. Spaniers book is a wonderful treatment of many important ideas in algebraic topology, from covering spaces to cech cohomology. However, for their detailed study, the books adhikari and adhikari basic modern algebra with applications, 2014, dugundji topology, 1966, herstein topics in algebra, 1964, maunder algebraic topology, 1970, spanier algebraic topology, 1966, and some other books are referred in bibliography. I found his chapters on algebraic topology especially the covering space chapter to be quite dry and unmotivated. Aug 17, 1990 intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology.
Of course it does not include some of the new developments, but these are anyway too advanced to be included in an introduction to the subject. The first part covers the material for two introductory courses about homotopy and homology. Introduction to algebraic topology and algebraic geometry. Algebraic topology ii mathematics mit opencourseware. Apart from that when spaniers book was written, the foundations of algebraic topology were already laid down. Our goal is to help bring people together so that they can collaborate. The more and more algebraic topology that i learn the more i continue to come back to hatcher for motivation and examples. Spanier, 9780387944265, available at book depository with free delivery worldwide. The second part of the book introduces the beginnings of algebraic topology. The first third of the book covers the fundamental group, its definition and its application in the study. The focus then turns to homology theory, including cohomology, cup products, cohomology operations, and topological manifolds. Nov 15, 2001 great introduction to algebraic topology.
Jan 15, 2016 this is an introductory course in algebraic topology. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. It meets its ambitious goals and should succeed in leading a lot of solid graduate students, as well as working mathematicians from other specialties seeking to learn this. I read about half of it, and it never felt like an old book. A good book for an introduction to algebraic topology. However, in my comment i was a bit too hasty about the continuity for cech cohomology. The curriculum is designed to acquaint students with fundamental mathematical. Jun 11, 2012 if you dont, kosniowski has a nice treatment of pointset topology in first 14 of his book that is just enough to learn algebraic topology in either kosniowski or massey. Basic algebraic topology and its applications springerlink. This book covers almost everything needed for both courses, and is explained well with a lot of pictures. The first third of the book covers the fundamental group, its definition and its application in the study of covering spaces. The proofs are correct, but often too terse for graduate students.
In this second term of algebraic topology, the topics covered include fibrations, homotopy groups, the hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor. Basic algebraic topology mathematical association of america. Given its chronological and evolutionary trajectory, algebraic topology is arguably the twentieth centurys most emblematic mathematical subject well, perhaps algebraic geometry is a competitor for the title. Spanier s book is a wonderful treatment of many important ideas in algebraic topology, from covering spaces to cech cohomology. 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. For those who have never taken a course or read a book on topology, i think hatchers book is a decent starting point. To get an idea you can look at the table of contents and the preface printed version. All in all, i think basic algebraic topology is a good graduate text.
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