Making sense of holes in spaces using algebra

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dc.contributor.advisor Dawson, Robert J. MacG
dc.creator Walker, Alexander P.
dc.date.accessioned 2024-06-18T14:36:20Z
dc.date.available 2024-06-18T14:36:20Z
dc.date.issued 2024-05-04
dc.identifier.uri http://library2.smu.ca/xmlui/handle/01/31958
dc.description 1 online resource (29 pages) : illustrations
dc.description Includes abstract.
dc.description Includes bibliographical references (pages 28-29).
dc.description.abstract Algebraic topology provides a nice method for detecting holes in topological spaces by the use of algebra. It turns out that algebra and holes are related to each other by groups: the fundamental group and homology group. On the matter of the fundamental group, there is a generalization to higher dimensions, called higher homotopy groups. In practice these are more difficult to compute, leading the discussion to go in the direction of homology groups, which are easier to compute. In doing this, we address the two varieties of homology groups, called simplicial and singular homology groups. Even though homology groups are easier to compute, we have to work hard to construct them. To remedy this, we turn to the Eilenberg-Steenrod approach which takes the properties of homology as axioms. en_CA
dc.description.provenance Submitted by Greg Hilliard (greg.hilliard@smu.ca) on 2024-06-18T14:36:20Z No. of bitstreams: 1 Walker_Alexander_Honours_2024.pdf: 363537 bytes, checksum: 6e5be60caa806a9bd1e0ac39472cb05e (MD5) en
dc.description.provenance Made available in DSpace on 2024-06-18T14:36:20Z (GMT). No. of bitstreams: 1 Walker_Alexander_Honours_2024.pdf: 363537 bytes, checksum: 6e5be60caa806a9bd1e0ac39472cb05e (MD5) Previous issue date: 2024-05-04 en
dc.language.iso en en_CA
dc.publisher Halifax, N.S. : Saint Mary's University
dc.title Making sense of holes in spaces using algebra en_CA
dc.type Text en_CA
thesis.degree.name Bachelor of Science (Honours Mathematics)
thesis.degree.level Undergraduate
thesis.degree.discipline Mathematics and Computing Science
thesis.degree.grantor Saint Mary's University (Halifax, N.S.)
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