Topological Slice Structures in Calabi–Yau Manifolds

We propose a structural framework for organizing the submanifold content of compact Calabi–Yau manifolds through the notion of a {Topological Slice Structure} (TSS), a coherent collection of calibrated submanifolds compatible with the Ricci-flat metric data. The central result is a decomposition principle asserting that, under mild conditions on the K”ahler polarization, such a structure exists, its cohomology classes span the full integer homology, and it is covariant with respect to mirror symmetry. Special cases recover special Lagrangian torus fibrations, divisors, and holomorphic curves as natural constituents of a unified geometric datum. We illustrate the framework through worked examples, introduce a numerical slice complexity invariant, and discuss implications for D-brane wrapping and moduli stabilization in string compactifications.