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

Geometry Topology

By William Fulton

To the instructor. This publication is designed to introduce a pupil to a few of the real rules of algebraic topology by way of emphasizing the re­ lations of those principles with different parts of arithmetic. instead of selecting one standpoint of modem topology (homotopy concept, simplicial complexes, singular idea, 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 variety of significant beneficial properties 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 now not aiming to turn into working towards algebraic topol­ ogists-without, we are hoping, discouraging budding topologists. We additionally suppose that this strategy is in greater concord with the ancient devel­ opment of the topic. What could we adore a scholar to understand after a primary path in to­ pology (assuming we reject the reply: half what one would prefer the coed to grasp after a moment path in topology)? Our solutions to this have guided the alternative of fabric, along with: less than­ status the relation among homology and integration, first on airplane domain names, in a while Riemann surfaces and in greater dimensions; wind­ ing numbers and levels of mappings, fixed-point theorems; appli­ cations corresponding to the Jordan curve theorem, invariance of area; in­ dices of vector fields and Euler features; primary groups

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