2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147614A recent anomaly computation of Horava and Witten is proved and generalized in the form of two index theorems in odd dimensions. Theorem A is a fixed point formula for orientation-reversing involutions. Theorem B is an index theorem for manifolds with boundary using local boundary conditions. Both hold for families of operators.12 pages, AMSTeX, date correctedDifferential GeometryHigh Energy Physics - Theorytext