The purpose of this thesis is to construct the homology groups of a complex over an R-module. The thesis begins with hyperplanes in Euclidean n-space. Simplexes and complexes are defined, and orientations are given to each simplex of a complex. The chains of a complex are defined, and each chain is assigned a boundary. The function which assigns to each chain a boundary defines the set of r-dimensional cycles and the set of r—dimensional bounding cycles. The quotient of those two submodules is the r-dimensional homology group.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc131634 |
| Date | 08 1900 |
| Creators | Chang, Chih-Chen |
| Contributors | Lau, Yiu Wa, Hagan, Melvin R. |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | 2, iii, 60 leaves, Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Chang, Chih-Chen |
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