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Research done and presented in relation to "Cubulated Holonomy", our chosen direction of research at the IU Bloomington 2024 REU. Mentor: Seppo Niemi Colvin Collaborator: Josue Molina

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%% Examples of how to add theorem-like statements 

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\newtheoremstyle{statement}{3pt}{3pt}{}{}{\bfseries}{:}{.5em}{}

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\newtheorem{thm}{Theorem}[section]  % theorems will be numbered in order

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\newtheorem{definition}{Definition}[section] % definitions will be numbered in order independently from theorems, and using [section] as optional third argument means the numbering is within sections

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\newtheorem{property}{Property}[section]

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\newtheorem{lemma}[thm]{Lemma} % using [thm] as optional second argument ensures that lemmas and theorems will be numbered together (i.e. using \thm and then \lemma will lead to Theorem 1 and Lemma 2)  

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\newtheorem*{remark*}{Remark} % use * to avoid numbering (ex. remarks will not have numbering like theorems do)  

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\newtheorem{prop}[thm]{Propositon}

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\newtheorem{corollary}[thm]{Corollary}

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%% Examples of macros 

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\newenvironment{atmProof}{\noindent\ignorespaces\paragraph{\textbf{Proof:}}}{\hfill \ding{122}\par\noindent}

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\def \R {\mathbb{R}} % macro for set of real numbers 

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\def \Z {\mathbb{Z}} % macro for set of integers

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\def \Q {\mathbb{Q}} % macro for set of rational numbers

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\def \C {\mathcal{C}}

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\DeclareMathOperator{\sd}{sd}

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\DeclareMathOperator{\st}{st}

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