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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