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DC Field | Value | Language |
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dc.contributor.author | Carroll, Ryan Andrew Edward | - |
dc.date.accessioned | 2012-05-23T20:07:07Z | - |
dc.date.available | 2012-05-23T20:07:07Z | - |
dc.date.issued | 2012-05 | - |
dc.identifier.uri | http://hdl.handle.net/10267/13673 | - |
dc.description | The author granted permission for the digitization of this paper. It was submitted by CD. | en_US |
dc.description.abstract | The project described here is a continuation of the work of several authors on orbifold invariants in low-dimensional and algebraic topology. Speci cally, my research explores applying the Euler-Satake characteristic to the {sectors of an orbifold for a nitely-generated group which results in a numerical invariant of the original orbifold, the {Euler-Satake characteristic. Most Euler characteristics have proven ine ective in giving useful information on orbifolds and, in particular, 3{orbifolds. Orbifolds can be partitioned into two categories: orientable and non-orientable. This partition is determined by the types of singularities in the orbifolds. My work previous to this project has dealt with formulating this invariant for orientable 3{orbifolds which lead to the successful determination of their point singularities when = F`, the free group of ` generators (see [3]). By now considering non-orientable 3{orbifolds, we have developed a formulation of the {Euler{Satake characteristic for all closed, e ective 3{orbifolds. In light of these formulas, counterexamples exist to show that neither an in nite collection of F`{ nor Z`{Euler{Satake characteristics determine the point singularities of general closed 3{orbifolds. Furthermore, counterexamples exist which prove that even an in nite collection of both F`{ and Z`{Euler{Satake characteristics do not determine the point singularities of general closed 3{orbifolds. | en_US |
dc.description.sponsorship | This paper was read and approved by Drs. Christopher Seaton, Rachel Dunwell, David Rupke, and Michael Sheard. | en_US |
dc.publisher | Memphis, Tenn. : Rhodes College | en_US |
dc.rights | Rhodes College owns the rights to the archival digital objects in this collection. Objects are made available for educational use only and may not be used for any non-educational or commercial purpose. Approved educational uses include private research and scholarship, teaching, and student projects. For additional information please contact archives@rhodes.edu. Fees may apply. | - |
dc.subject | Text | - |
dc.subject | Honors papers | en_US |
dc.subject | Mathematics and Computer Science, Department of | en_US |
dc.subject | Student research | en_US |
dc.title | Extensions of the Euler-Satake Characteristic of Closed 3-Orbifolds | en_US |
dc.type | Thesis | en_US |
Appears in Collections: | Honors Papers |
Files in This Item:
File | Description | Size | Format | |
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Carroll_Ryan_Honors_2012.pdf | 4.06 MB | Adobe PDF | View/Open |
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