Complex Analysis on Planar Cell Complexes
Rachel Florence Arnold · 2008
(ABSTRACT) This paper is an examination of the theory of discrete complex analysis that arises from the framework of a planar cell complex. Construction of this theory is largely integration-based. A combination of two cell complexes, the double and its associated diamond complex, allows for the development of a discrete Cauchy Integral Formula. Acknowledgments I cannot even begin to express the extreme gratitude that I have for the unfailing support, encouragement, and strong leadership of my thesis advisor, Dr. Peter Haskell. Through his careful and patient guidance, Dr. Haskell instilled confidence in my research abilities and cultivated my mathematical creativity, giving me the courage to ask difficult and motivating questions. I am also genuinely thankful for the time and effort spent by Dr. Edward Green and Dr. Jim Thomson, members of my Masters Thesis Committee, in reviewing this paper. iii