By Fred H. Croom
This article is meant as a one semester creation to algebraic topology on the undergraduate and starting graduate degrees. essentially, it covers simplicial homology thought, the basic team, overlaying areas, the better homotopy teams and introductory singular homology idea. The textual content follows a large ancient define and makes use of the proofs of the discoverers of the $64000 theorems while this can be in line with the user-friendly point of the path. this system of presentation is meant to minimize the summary nature of algebraic topology to a degree that's palatable for the start pupil and to supply motivation and unity 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 thoughts via utilising 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 before everything engaged on the appendices, yet really that he learn from the start of the textual content, pertaining to the appendices as his reminiscence wishes clean. The textual content is designed to be used by means of university juniors of ordinary intelligence and doesn't require "mathematical adulthood" past the junior point.
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