Addendum to “A new proof of the Bott periodicity theorem”: [Topology Appl. 119 (2002) 167–183]

A. Elmendorf has found an error in the approach to Lemmas 2.2 and 2.3 of “A new proof of the Bott periodicity theorem” (Topology and its Applications, 2002, 167–183). There are also errors in the definitions of the maps in Sections 4.2 and 4.5. In this paper we supply corrections to these errors. We also sketch a major simplification of the argument proving real Bott periodicity, unifying the eight quasifibrations appearing in the real case, using Clifford algebras.