By William Fulton

To the instructor. This publication is designed to introduce a pupil to a few of the \$64000 rules of algebraic topology through emphasizing the re­ lations of those rules with different components of arithmetic. instead of determining one viewpoint of modem topology (homotopy conception, simplicial complexes, singular thought, axiomatic homology, vary­ ential topology, etc.), we focus our cognizance on concrete prob­ lems in low dimensions, introducing merely as a lot algebraic machin­ ery as helpful for the issues we meet. This makes it attainable to work out a greater variety of significant positive aspects of the topic than is common in a starting textual content. The ebook is designed for college kids 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 procedure is in larger concord with the ancient devel­ opment of the topic. What may we love a scholar to grasp after a primary direction in to­ pology (assuming we reject the reply: half what one would prefer the coed to understand after a moment path in topology)? Our solutions to this have guided the alternative of fabric, together with: below­ status the relation among homology and integration, first on aircraft domain names, in a while Riemann surfaces and in larger dimensions; wind­ ing numbers and levels of mappings, fixed-point theorems; appli­ cations similar to the Jordan curve theorem, invariance of area; in­ dices of vector fields and Euler features; basic groups

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