2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138314The grassmannian of hermitian lagrangian spaces in $\mathbb{C}^n\oplus \mathbb{C}^n$ is a natural compactification of the space of hermitian $n\times n$ matrices. We describe a Schubert-like, Whitney regular stratification on this space which has a Morse theoretic origin. We prove that these strata define closed subanalytic currents à la R. Hardt, generating the integral homology of this space, we investigate their intersection theoretic properties, and we prove certain odd (in K-theoretic sense) Thom-Porteous type theorems.52 pages, 1 figure. Fixed typos, added new referencesGeometric TopologyAlgebraic TopologyDifferential Geometry32C30,49Q15, 57R19, 57T10, 58A35, 58E05text