By William S. Massey
"This publication is meant to function a textbook for a direction in algebraic topology first and foremost graduate point. the most themes coated are the category of compact 2-manifolds, the basic crew, overlaying areas, singular homology conception, and singular cohomology thought. those themes are constructed systematically, averting all pointless definitions, terminology, and technical equipment. anyplace attainable, the geometric motivation at the back of some of the suggestions is emphasised. The textual content involves fabric from the 1st 5 chapters of the author's prior publication, ALGEBRAIC TOPOLOGY: AN creation (GTM 56), including just about all of the now out-of-print SINGULAR HOMOLOGY concept (GTM 70). the cloth from the sooner books has been conscientiously revised, corrected, and taken as much as date."
Searchable DJVU with a bit askew pages.
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Extra info for A Basic Course in Algebraic Topology (Graduate Texts in Mathematics)
4 Showing the result of a move. square; whereas in (b) the orientation of the symbol tells you to flip the square over a vertical axis along the right-hand side of the square. 4 the heavy right-pointing arrow indicates that by performing the move on the left-hand figure (rotating the entire figure 90◦ in a clockwise direction about the right angle), we obtain the right-hand figure. C. the Greeks were fascinated with the idea of constructing regular N -gons with Euclidean tools (straightedge and compass).
We’ll wait. Look at your flexagon. Observe that there are subtle differences between the 2 visible faces. 9. Surprisingly, this flexagon can change its shape. 10. Of course, after you have gone from left to right you will need to reverse the moves to get the flexagon back into its original shape. You may wish to practice these procedures until you have a feel for them. Take your time. Then come back and we’ll tell you how to flex your 8-flexagon in ways similar to your procedures with the 6-flexagon.
In the next paragraph we describe two aspects of our paper-folding, and building, instructions where we do advise rather rigid adherence to our specifications. However, we are very far from recommending that you fold all your regular polygons and construct all your polyhedra exactly as described. What we have done is to give you algorithms for the relevant constructions. Machines follow algorithms with relentless fervor, while human beings look for special ways of doing particular, convenient things.
A Basic Course in Algebraic Topology (Graduate Texts in Mathematics) by William S. Massey