周環
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