We study the sl(3) web algebra via morphisms on foams. A pre-foam is a cobordism between two webs that contains singular arcs, which are sets of points whose neighborhoods are homeomorphic to the cross-product of the letter "Y'' and the unit interval. Pre-foams may have a distinguished point, and it can be moved around as long as it does not cross a singular arc. A foam is an isotopy class of pre-foams modulo a set of certain relations involving dots on the pre-foams. Composition in Foams is achieved by stacking pre-foams. We compute the cohomology ring of the sl(3) web algebra and apply a functor from the cohomology ring of the sl(3) web algebra to {\bf Foams}. Afterwards, we use this to study the $\mathfrak{sl}(3)$ web algebra via morphisms on foams.
| Identifer | oai:union.ndltd.org:uiowa.edu/oai:ir.uiowa.edu:etd-5797 |
| Date | 01 May 2015 |
| Creators | Salazar-Torres, Dido Uvaldo |
| Contributors | Frohman, Charles D. |
| Publisher | University of Iowa |
| Source Sets | University of Iowa |
| Language | English |
| Detected Language | English |
| Type | dissertation |
| Format | application/pdf |
| Source | Theses and Dissertations |
| Rights | Copyright 2015 Dido Salazar-Torres |
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