Crispy, D. Glaze, T. Filling, M. Sprinkle, K. Dunkin, B.
In this paper, we consider the age-old mathematical question: What do doughnuts and homological algebra have in common? Our investigation combines the topological properties of doughnuts with the abstract language of homological algebra. We start by examining the shape of a doughnut, or torus, and its fundamental group. Adding frosting and sprinkles does not change the homotopy type, but it does make the doughnut more delicious. Using homological algebra, we prove that a box of doughnuts is homotopy equivalent to a single doughnut, as long as you eat them all at once. In conclusion, our findings suggest that doughnuts and homological algebra are not so different after all - both are full of unexpected twists, turns, and holes.