New PDF release: Algebraic Topology: A First Course (Graduate Texts in

By William Fulton

ISBN-10: 0387943277

ISBN-13: 9780387943275

To the instructor. This publication is designed to introduce a scholar to a few of the real principles of algebraic topology by way of emphasizing the re­ lations of those principles with different components of arithmetic. instead of deciding upon one standpoint of modem topology (homotopy conception, simplicial complexes, singular conception, axiomatic homology, fluctuate­ 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 beneficial 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 e-book is designed for college students of arithmetic or technological know-how who're now not aiming to develop into practising algebraic topol­ ogists-without, we are hoping, discouraging budding topologists. We additionally consider that this strategy is in greater concord with the ancient devel­ opment of the topic. What could we adore a pupil to grasp after a primary direction in to­ pology (assuming we reject the reply: half what one would prefer the scholar to understand after a moment path in topology)? Our solutions to this have guided the alternative of fabric, inclusive of: below­ status the relation among homology and integration, first on airplane domain names, in a while Riemann surfaces and in better dimensions; wind­ ing numbers and levels of mappings, fixed-point theorems; appli­ cations equivalent 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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