For example, in topology, many examples of gerbes can be constructed by considering gerbes banded by the group formula_55. As the classifying space formula_56 is the second Eilenberg-Maclane space for the integers, a bundle gerbe banded by formula_55 on a topological space formula_39 is constructed from a homotopy class of maps informula_59which is exactly the third singular homology group formula_60. It has been found that all gerbes representing torsion cohomology classes in formula_60 are represented by a bundle of finite dimensional algebras formula_62 for a fixed complex vector space formula_63. In addition, the non-torsion classes are represented as infinite-dimensional principal bundles formula_64 of the projective group of unitary operators on a fixed infinite dimensional separable Hilbert space formula_65. Note this is well defined because all separable Hilbert spaces are isomorphic to the space of square-summable sequences formula_66.