Date of Award
1995
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Patrick Gilmer
Abstract
Blanchet, Habegger, Masbaum and Vogel defined a quantization functor on a category whose objects are oriented closed surfaces together with a collection of colored banded points and $p\sb1$-structure. The functor assigns a module $V\sb{p}(\Sigma)$ to each surface $\Sigma$. This assignment satisfies certain axioms. For p even, it satisfies the tensor product axiom, which gives the modules associated to a disconnected surface as the tensor-product of the modules associated to its components. In this dissertation we show that the p odd case satisfies a generalized tensor product formula. The notion of a generalized tensor product formula is due to Blanchet, and Masbaum. We let $\ V\sb{p}(\Sigma)$ denote $V\sb{p}(\Sigma{\rm II}\widehat{S\sp2}),$ where $\widehat{S\sp2}$ is a sphere with one banded point colored p-2. The generalized tensor product formula expresses $V\sb{p}(\Sigma\sb1{\rm II}\Sigma\sb2)$ in terms of $V\sb{p}(\Sigma\sb1),\ V\sb{p}(\Sigma\sb2),\ \ V\sb{p}(\Sigma\sb1),$ and $\ V\sb{p}(\Sigma\sb2).$ We reduce the calculation of $\ V\sb{p}(\Sigma)$ to known results, and calculate $\ V\sb{p}(\Sigma)$ explicitly in many cases. We consider the application of this theory to links of odd wrapping number in $S\sp1 \times S\sp2.$.
Recommended Citation
Chimitza, Basinyi, "Modules Associated to Disconnected Surfaces by Quantization Functors." (1995). LSU Historical Dissertations and Theses. 6001.
https://repository.lsu.edu/gradschool_disstheses/6001
Pages
48
DOI
10.31390/gradschool_disstheses.6001