2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55404A topological fact about eleven dimensions is used to motivate a potential new duality in M-theory. We complete the discussion of consistent limits of M-theory raised in a previous paper to include gravitational anomaly cancelation and four-form flux quantization in the context of the $M^{10}\times S^1/Z_2$ compactifications. A suprise is found: If one includes a $Z_2$ anomaly which exists only in 8k+3 dimensions then there are two distinct quantum limits, one related to each of two equivalency classes of the orbifolds $M^{10}\times S^1/Z_2$.11 pages, LaTeX, minor typos correctedHigh Energy Physics - Theorytext