Download e-book for kindle: Algebraic Topology: An Introduction by William S. Massey

By William S. Massey

ISBN-10: 0387902716

ISBN-13: 9780387902715

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William S. Massey Professor Massey, born in Illinois in 1920, acquired his bachelor's measure from the college of Chicago after which served for 4 years within the U.S. army in the course of international battle II. After the conflict he got his Ph.D. from Princeton collage and spent extra years there as a post-doctoral study assistant. He then taught for ten years at the college of Brown college, and moved to his current place at Yale in 1960. he's the writer of diverse study articles on algebraic topology and similar issues. This publication built from lecture notes of classes taught to Yale undergraduate and graduate scholars over a interval of a number of years.

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We assert that we can number the triangles T1, T2, . -_1, 2 g 2' g 11.. 1 / l9 angles T1; for T2 choose any triangle that has an edge in common with T1, for T3 choose any triangle that has an edge in common with T1 or T2, etc. If at any stage we could not continue this process, then we would have two sets of triangles {T1, . , Th}, and {Tk+1, . , Tn} such that no triangle in the first set would have an edge or vertex in common with any triangle of the second set. But this would give a partition of S into two disjoint nonempty closed sets, contrary to the assumption that S was connected.

It is a hexagon) and such that distinct regions have no more than one side in common. 6 Let SI be a surface that is the sum of m tori, m g 1, and let S, be a surface that is the sum of n projective planes, n _2_ 1. Suppose two holes are cut in each of these surfaces, and the two surfaces are then glued together along the boundaries of the holes. What surface is obtained by this process? 7 What surface is represented by a regular 10-gon with edges identified in pairs, as indicated by the symbol abcdec‘lda‘lb‘le‘l?

T; are pairwise disjoint; if they are not, we can translate some of them to various other parts of the plane R2. Let T’ = UTQ; then T’ is a compact subset of R2. Define a map go : T’ ——> S by go I T; = goi; the map go is obviously continuous and onto. Because T’ is compact and S is a Hausdorff space, go is a closed map, and hence S has the quotient topology determined by go (see Section 1 of Appendix A). This is a rigorous mathematical statement of our intuitive idea that S is obtained by gluing the triangles T1, T2, .

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Algebraic Topology: An Introduction by William S. Massey


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