By William Fulton

To the instructor. This booklet is designed to introduce a scholar to a few of the real principles of algebraic topology via emphasizing the re lations of those rules with different components of arithmetic. instead of opting for one viewpoint of modem topology (homotopy conception, simplicial complexes, singular idea, axiomatic homology, range ential topology, etc.), we focus our recognition on concrete prob lems in low dimensions, introducing in basic terms as a lot algebraic machin ery as worthy 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 students of arithmetic or technology 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 historic 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: half what one would prefer the scholar to grasp after a moment direction in topology)? Our solutions to this have guided the alternative of fabric, which include: below status the relation among homology and integration, first on aircraft domain names, afterward Riemann surfaces and in better dimensions; wind ing numbers and levels of mappings, fixed-point theorems; appli cations akin to the Jordan curve theorem, invariance of area; in dices of vector fields and Euler features; primary teams