Browsing by Author "Davis, Christopher"

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    First Order Signatures and Knot Concordance
    (2012-09-05) Davis, Christopher; Cochran, Tim D.; Harvey, Shelly; Borcea, Liliana
    Invariants of knots coming from twisted signatures have played a central role in the study of knot concordance. Unfortunately, except in the simplest of cases, these signature invariants have proven exceedingly difficult to compute. As a consequence, many knots which presumably can be detected by these invariants are not a well understood as they should be. We study a family of signature invariants of knots and show that they provide concordance information. Significantly, we provide a tractable means for computing these signatures. Once armed with these tools we use them first to study the knot concordance group generated by the twist knots which are of order 2 in the algebraic concordance group. With our computational tools we can show that with only finitely many exceptions, they form a linearly independent set in the concordance group. We go on to study a procedure given by Cochran-Harvey-Leidy which produces infinite rank subgroups of the knot concordance group which, in some sense are extremely subtle and difficult to detect. The construction they give has an inherent ambiguity due to the difficulty of computing some signature invariants. This ambiguity prevents their construction from yielding an actual linearly independent set. Using the tools we develop we make progress to removing this ambiguity from their procedure.
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    The Religious Community and Latinos in Alabama: Two Steps Forward
    (2013-12-06) Davis, Christopher; Boles, John B.; Cox, Edward; Aranda, Jose F., Jr.
    This dissertation explores the nuances of how the religious community of Alabama responded to the development of a Latino population in the state, beginning in the mid-1980s, as well as how Latinos found a place among the preexisting religious institutions. Much of the academic focus on Latinos in the South has explored the topic from the perspectives of labor, politics, housing, and other lenses that typically revealed negative interactions between Latinos and the long-term population. Also, studies of religious matters generally focus on the Catholic Church, which included the majority of the Latino population but left out much of the interaction with the mostly Protestant majority. Through interviews with congregation leaders, this study shows that the incorporation of Latinos was a complex process based in a history and experience of missions work. Beginning in the 1950s, the understanding of missions began to change from long-term missions undertaken by few Christians to mostly short-term missions experienced by many. That missions background made the possibility of ministering to Latinos in Alabama much more plausible and led to the partnerships discussed in the rest of the dissertation. The part of the state to first receive Latinos was the northeast corner where the religious community initially responded to migrant Latinos beginning in the 1950s and then to a permanent Latino population in the 1980s. The study also focuses on the city of Birmingham and finds that strong leaders were the crucial element in developing Latino ministries. Such partnerships resulted in great variety among the structures of ministries based on the abilities and desires of the individual churches. The relationships formed in the church environment served as a counter to the state and national vitriol concerning illegal immigration and produced a state population with mixed feelings about its Latino component. Those relations also provided hope for the eventual partnership of all races.