“Bott and Tu give us an introduction to algebraic topology via differential forms, imbued with the spirit of a master who knew differential forms way back when, yet . Text: Raoul Bott and Loring W. Tu, Differential Forms in Algebraic Topology, 3rd Algebraic topology offers a possible solution by transforming the geometric. The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. Accord ingly, we.
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The force of this technique is demonstrated by the fact that the authors at the end of this chapter arrive at a really comprehensive exposition of Poincare duality, the Euler and Thom classes and the Thom isomorphism.
Goodreads is the world’s largest site for readers with over 50 million reviews. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
The authors invite the reader to understand algebraic topology by completing himself proofs and examples in the exercises. So I personally don’t think you will need some extra-book with exercises. Other books in this series. Riemannian Geometry Peter Petersen.
I can recommend Hatcher’s book though it is again a bit too wordy in my opinionor these notes by Sossinsky. Home Contact Us Help Free delivery worldwide.
Introduction to Topological Manifolds John M.
Differential Forms in Algebraic Topology
Differential Forms in Algebraic Topology by Bott and Tu | Physics Forums
Tu No preview available – Home Questions Tags Users Unanswered. We offer it topoloyg the hope that such an informal account of the subject at a semi-introductory level fills a gap in the literature. Riemannian Manifolds John M. Dispatched from the UK in 3 business days When will my order arrive? Looking for beautiful books? Although we have in mind an audience with prior exposure to algebraic or differential topology, for the most part a good knowledge of linear algebra, advanced calculus, and point-set topology should suffice.
If you will need some extra-stuff, you can always look it up. Accord ingly, we move primarily in the realm of smooth nott and use the de Rham theory as a prototype of all of cohomology.
Because, if you only want to begin studying algebraic topology, I strongly suggest to start from Hatcher. The first chapter contains the de Rham theory, with stress on computability.
They are not following Bott-Tu book, but there are bptt lot of common topics. So it would be difficult to read if you don’t know what differential forms really are.
Speaking about exercises in Bott-Tu, there are indeed not too many of them, and most of them are pretty easy. But if you will feel that you need some more problems on algebraic topology, there are a lot of nice books.
Altogether it is only about 50 pages, and I think Warner gives a concise and clear introduction to the subject. Topology and Geometry Glen E. The third chapter on spectral sequences is the most difficult one, but also the richest one by the various applications and digressions into other topics of algebraic topology: Representation Theory William Fulton. Certain sections may be omitted at first reading with out loss of continuity.
Review quote “Bott and Tu give us an introduction to algebraic topology via differential forms, imbued with the spirit of a master who knew differential forms way back when, yet written from a mature point of view which draws together the separate paths traversed by de Rham theory and homotopy theory.
Email Required, but never shown. Sasha Patotski 4, 1 14 I’ve never done the exercises from Bott-Tu, but I think your background is sufficient if you know basic facts about manifolds. The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. The last chapter is devoted to a brief and comprehensive description of the Chern and Pontryagin classes.
Sign up using Facebook. This book is not intended to be foundational; rather, it is only meant to open some of the doors to the formidable edifice of modern algebraic topology. You would definitely need some basic understanding of manifolds, but I don’t think you will need too much.
Differential Forms in Algebraic Topology : Raoul Bott :
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