By William Fulton

To the trainer. This publication is designed to introduce a pupil to a couple of the real rules of algebraic topology via emphasizing the re­ lations of those rules with different components of arithmetic. instead of settling on one viewpoint of modem topology (homotopy idea, simplicial complexes, singular concept, axiomatic homology, fluctuate­ ential topology, etc.), we focus our consciousness on concrete prob­ lems in low dimensions, introducing simply as a lot algebraic machin­ ery as worthwhile for the issues we meet. This makes it attainable to work out a greater diversity of vital positive aspects of the topic than is common in a starting textual content. The publication is designed for college kids of arithmetic or technological know-how who're no longer aiming to develop into working towards algebraic topol­ ogists-without, we are hoping, discouraging budding topologists. We additionally suppose that this process is in larger concord with the historic devel­ opment of the topic. What could we adore a pupil to grasp after a primary path in to­ pology (assuming we reject the reply: 1/2 what one would prefer the coed to grasp after a moment path in topology)? Our solutions to this have guided the alternative of fabric, including: below­ status the relation among homology and integration, first on aircraft domain names, afterward Riemann surfaces and in greater 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; primary groups

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

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