Algebraic Topology - (Graduate Texts in Mathematics) by William Fulton (Paperback)
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<p/><br></br><p><b> Book Synopsis </b></p></br></br>To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol- ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel- opment of the subject. What would we like a student to know after a first course in to- pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under- standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind- ing numbers and degrees of mappings, fixed-point theorems; appli- cations such as the Jordan curve theorem, invariance of domain; in- dices of vector fields and Euler characteristics; fundamental groups<p/><br></br><p><b> Review Quotes </b></p></br></br><br>W. Fulton <P>Algebraic Topology <P>A First Course <P>"Fulton has done genuine service for the mathematical community by writing a text on algebraic topology which is genuinely different from the existing texts. Each time a text such as this is published we more truly have a real choice when we pick a book for a course or for self-study. The author, who is an expert in algebraic geometry, has given us his own personal idiosyncratic vision of how the subject should be developed."a "AMERICAN MATHEMATICAL MONTHLY<br><br><P>W. Fulton <P>Algebraic Topology <P>A First Course <P>"Fulton has done genuine service for the mathematical community by writing a text on algebraic topology which is genuinely different from the existing texts. Each time a text such as this is published we more truly have a real choice when we pick a book for a course or for self-study. The author, who is an expert in algebraic geometry, has given us his own personal idiosyncratic vision of how the subject should be developed."???AMERICAN MATHEMATICAL MONTHLY<br><br>W. Fulton<P>Algebraic Topology<P>A First Course<P>"Fulton has done genuine service for the mathematical community by writing a text on algebraic topology which is genuinely different from the existing texts. Each time a text such as this is published we more truly have a real choice when we pick a book for a course or for self-study. The author, who is an expert in algebraic geometry, has given us his own personal idiosyncratic vision of how the subject should be developed."AMERICAN MATHEMATICAL MONTHLY<br>
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