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We give a general method for constructing compact K\"ahler manifolds $X_1$and $X_2$ whose intermediate Jacobians $J^k(X_1)$ and $J^k(X_2)$ are isogenousfor each $k$, and we exhibit some examples. The method is based upon thealgebraic transplantation formalism arising from Sunada's technique forconstructing pairs of compact Riemannian manifolds whose Laplace spectra arethe same. We also show that the method produces compact Riemannian manifoldswhose Lazzeri Jacobians are isogenous.

Transplantation and isogeny of intermediate Jacobians of compact K\"ahler manifolds