Baker, D. Crumbs, S. Fry, K. Gloop, M. Powder, A.
In this paper, we use homological algebra to explore the topological properties of doughnuts. We begin by defining the ring of polynomials over the field of glazed donuts, and then introduce some basic concepts from homological algebra, such as cohomology and the snake lemma. Next, we examine the algebraic structure of doughnuts by looking at their holes. By constructing a simplicial complex of donuts, we are able to calculate the Euler characteristic of different types of donuts. To our surprise, we discovered that the topological properties of a doughnut vary greatly depending on its frosting-to-hole ratio. In particular, we prove that sprinkles have a significant impact on the homology groups. Overall, this paper demonstrates the incredible complexity of the humble doughnut and the power of homological algebra to unravel its mysteries.