This is an announcement for the paper "Conditions implying the uniqueness of the weak$^*$-topology on certain group algebras" by Matthew Daws, Hung Le Pham and Stuart White. Abstract: We investigate possible preduals of the measure algebra $M(G)$ of a locally compact group and the Fourier algebra $A(G)$ of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the multiplication separately weak$^*$-continuous so that these algebras are dual Banach algebras. In this paper we find additional conditions under which the preduals $C_0(G)$ of $M(G)$ and $C^*(G)$ of $A(G)$ are uniquely determined. In both cases we consider a natural coassociative multiplication and show that the canonical predual gives rise to the unique weak$^*$-topology making both the multiplication separately weak$^*$-continuous and the coassociative multiplication weak$^*$-continuous. In particular, dual cohomological properties of these algebras are well defined with this additional structure. Archive classification: math.FA math.OA Mathematics Subject Classification: 43A20, 43A77 Remarks: 21 pages The source file(s), UniquePredualFinalDraft2.tex: 73814 bytes, is(are) stored in gzipped form as 0804.3764.gz with size 22kb. The corresponding postcript file has gzipped size 133kb. Submitted from: matt.daws@cantab.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3764 or http://arXiv.org/abs/0804.3764 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3764 or in gzipped form by using subject line get 0804.3764 to: math@arXiv.org.