How the exterior algebra captures essences of topology, Lie theory,
combinatorics, and algebraic geometry.
Abstract:
We survey how the exterior algebra encodes triangulations and homology in
topology, how giving it a differential graded structure is equivalent
to giving a Lie algebra, how the cohomology ring of a complex hyperplane arrangement is a
quotient of the exterior algebra, and how exterior algebra resolutions encode the cohomology
of coherent sheaves on projective spaces.