Download e-book for iPad: Algebraic Topology: A First Course (Graduate Texts in by William Fulton

By William Fulton

To the instructor. This booklet is designed to introduce a scholar to a couple of the $64000 rules of algebraic topology via emphasizing the re­ lations of those principles with different parts of arithmetic. instead of opting for one perspective of modem topology (homotopy thought, simplicial complexes, singular concept, axiomatic homology, range­ ential topology, etc.), we focus our realization on concrete prob­ lems in low dimensions, introducing in simple terms as a lot algebraic machin­ ery as important for the issues we meet. This makes it attainable to work out a greater diversity of vital beneficial properties of the topic than is common in a starting textual content. The ebook is designed for college students of arithmetic or technology who're no longer aiming to develop into practising algebraic topol­ ogists-without, we are hoping, discouraging budding topologists. We additionally think that this strategy is in greater concord with the old devel­ opment of the topic. What might we love a pupil to grasp after a primary path in to­ pology (assuming we reject the reply: 1/2 what one would prefer the scholar to understand after a moment direction in topology)? Our solutions to this have guided the alternative of fabric, such as: lower than­ status the relation among homology and integration, first on aircraft domain names, afterward Riemann surfaces and in larger dimensions; wind­ ing numbers and levels of mappings, fixed-point theorems; appli­ cations resembling the Jordan curve theorem, invariance of area; in­ dices of vector fields and Euler features; primary groups

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

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