  In 1997, N.M. Kumar published a paper which introduced a new tool of use in
the construction of algebraic vector bundles. Given a vector bundle on
projective n-space, a well known theorem of Quillen-Suslin guarantees the
existence of sections which generate the bundle on the complement of a
hyperplane in projective n-space. Kumar used this fact to give a correspondence
between vector bundles on projective n-space and vector bundles on projective
(n-1)-space satisfying certain conditions. He then applied this correspondence
to establish the existence of many, previously unknown, rank two bundles on
projective fourspace in positive characteristic. The goal of the present paper
is to give an explicit homological description of Kumar's correspondence in a
setting appropriate for implementation in a computer algebra system.
