  In this paper, we consider a variation on Cheeger numbers related to the
coboundary expanders recently defined by Dotterer and Kahle. A Cheeger-type
inequality is proved, which is similar to a result on graphs due to Fan Chung.
This inequality is then used to study the relationship between coboundary
expanders on simplicial complexes and their corresponding eigenvalues,
complementing and extending results found by Gundert and Wagner. In particular,
we find these coboundary expanders do not satisfy natural Buser or Cheeger
inequalities.
