2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51114In this article, we study how the Grothendieck group of coherent sheaves can be used to describe D-branes. We show how global bound state construction in topological $K$-theory can be adapted to our context, showing that D-branes wrapping a subvariety are holomorphically classified by a relative $K$-group. By taking the duality between the relative $K$-groups and the $K$-homologies, we show that D-brane charge of type IIB superstrings is properly classified by the $K$-homology.11pages, minor changes, references addedHigh Energy Physics - Theorytext