By William Fulton

ISBN-10: 0387943277

ISBN-13: 9780387943275

To the instructor. This ebook is designed to introduce a scholar to a few of the $64000 rules of algebraic topology by way of emphasizing the re­ lations of those rules with different components of arithmetic. instead of opting for one perspective of modem topology (homotopy thought, simplicial complexes, singular conception, axiomatic homology, range­ ential topology, etc.), we focus our recognition on concrete prob­ lems in low dimensions, introducing in simple terms as a lot algebraic machin­ ery as valuable for the issues we meet. This makes it attainable to determine a greater variety of significant good points of the topic than is common in a starting textual content. The booklet is designed for college students of arithmetic or technology who're no longer aiming to develop into training algebraic topol­ ogists-without, we are hoping, discouraging budding topologists. We additionally suppose that this technique is in larger concord with the ancient devel­ opment of the topic. What may we adore a scholar to understand after a primary direction in to­ pology (assuming we reject the reply: 1/2 what one would favor the scholar to grasp after a moment direction in topology)? Our solutions to this have guided the alternative of fabric, together with: lower than­ status the relation among homology and integration, first on airplane domain names, afterward Riemann surfaces and in better dimensions; wind­ ing numbers and levels of mappings, fixed-point theorems; appli­ cations comparable to the Jordan curve theorem, invariance of area; in­ dices of vector fields and Euler features; basic groups

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Algebraic Topology: A First Course (Graduate Texts in Mathematics) by William Fulton


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