Preprint · arXiv:2605.31831 [math.AT] · v4
M. R. Annulus, Department of Beverage Topology, Institute for Applied Pedantry.
Abstract. We settle, with what we concede is gratuitous machinery, the recurring popular question of how many holes are possessed by a standard drinking straw. The straw is homotopy equivalent to the circle; we therefore compute its homotopy groups, singular and de Rham cohomology rings, group (co)homology, complex and real K-theory, oriented bordism, stable homotopy, and an Alexander-dual linking invariant. For each theory we recall its definition and meaning, exhibit a short proof, and identify the resulting generator with the unique hole. Every invariant designed to count holes returns the same value, namely $1$. The two boundary circles occasionally mistaken for additional holes are demonstrated to be boundary, not topology.
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