Chow ring
There is an easy description of the cohomology ring, or the Chow ring, of the Grassmannian using the Chern classes of two natural vector bundles over the grassmannian formula_6. There is a sequence of vector bundlesformula_75where formula_76 is the trivial vector bundle of rank formula_3, the fiber of formula_78 over formula_79 is the subspace formula_21, and formula_81 is the quotient vector bundle (which exists since the rank is constant on each of the fibers). The Chern classes of these two associated bundles areformula_82where formula_83 is an formula_52-tuple andformula_85The tautological sequence then gives the presentation of the Chow ring asformula_86