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

By William Fulton

To the instructor. This e-book is designed to introduce a pupil to a couple of the \$64000 principles of algebraic topology by means of emphasizing the re­ lations of those rules with different components of arithmetic. instead of picking out one perspective of modem topology (homotopy conception, simplicial complexes, singular thought, axiomatic homology, range­ ential topology, etc.), we focus our realization on concrete prob­ lems in low dimensions, introducing merely as a lot algebraic machin­ ery as beneficial for the issues we meet. This makes it attainable to determine a greater variety of significant positive aspects of the topic than is common in a starting textual content. The publication is designed for college kids of arithmetic or technology who're no longer aiming to turn into training algebraic topol­ ogists-without, we are hoping, discouraging budding topologists. We additionally consider that this technique is in greater concord with the old devel­ opment of the topic. What could we love a scholar to grasp after a primary direction in to­ pology (assuming we reject the reply: half what one would favor the coed to grasp after a moment direction in topology)? Our solutions to this have guided the alternative of fabric, which include: lower than­ status the relation among homology and integration, first on airplane domain names, in a while Riemann surfaces and in larger dimensions; wind­ ing numbers and levels of mappings, fixed-point theorems; appli­ cations comparable to the Jordan curve theorem, invariance of area; in­ dices of vector fields and Euler features; basic groups

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