$RO(C_3)$-graded Bredon Cohomology and $C_p$-surfaces
| dc.contributor.advisor | Dugger, Daniel | |
| dc.contributor.author | Pohland, Kelly | |
| dc.date.accessioned | 2022-10-04T19:31:55Z | |
| dc.date.available | 2022-10-04T19:31:55Z | |
| dc.date.issued | 2022-10-04 | |
| dc.description.abstract | Let $p$ be an odd prime, and let $C_p$ denote the cyclic group of order $p$. We use equivariant surgery methods to classify all closed, connected $2$-manifolds with an action of $C_p$. We then use this classification in the case $p=3$ to compute the $RO(C_3)$-graded Bredon cohomology of all $C_3$-surfaces in constant $\underline{\mathbb{Z}/3}$ coefficients as modules over the cohomology of a point. We show that the cohomology of a $C_3$-surface is completely determined by its genus, number of fixed points, and whether or not its underlying surface is orientable. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/27567 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.subject | algebraic topology | en_US |
| dc.subject | homotopy theory | en_US |
| dc.title | $RO(C_3)$-graded Bredon Cohomology and $C_p$-surfaces | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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