By Fred H. Croom
This article is meant as a one semester creation to algebraic topology on the undergraduate and starting graduate degrees. primarily, it covers simplicial homology idea, the elemental team, protecting areas, the better homotopy teams and introductory singular homology concept. The textual content follows a extensive historic define and makes use of the proofs of the discoverers of the $64000 theorems whilst this is often in keeping with the basic point of the path. this system of presentation is meant to lessen the summary nature of algebraic topology to a degree that's palatable for the start pupil and to supply motivation and team spirit which are frequently missing in abstact remedies. The textual content emphasizes the geometric method of algebraic topology and makes an attempt to teach the significance of topological innovations via employing them to difficulties of geometry and research. the necessities for this path are calculus on the sophomore point, a one semester advent to the speculation of teams, a one semester introduc tion to point-set topology and a few familiarity with vector areas. Outlines of the prerequisite fabric are available within the appendices on the finish of the textual content. it's endorsed that the reader now not spend time in the beginning engaged on the appendices, yet fairly that he learn from the start of the textual content, bearing on the appendices as his reminiscence wishes clean. The textual content is designed to be used by way of university juniors of standard intelligence and doesn't require "mathematical adulthood" past the junior point.
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