  Motivated by applications to higher-rank Brill-Noether theory and the
Bertram-Feinberg-Mukai conjecture, we introduce the concepts of linked
alternating and linked symplectic forms on a chain of vector bundles, and show
that the linked symplectic Grassmannians parametrizing chains of subbundles
isotropic for a given linked symplectic form has good dimensional behavior
analogous to that of the classical symplectic Grassmannian.
