Hovering over the Gmail icon would let you see your messages. Hover over Calendar for a quick look at what's on your agenda. Hover over the Spreadsheets, Documents, or Presentation icon to see the status of any of your files -- that is, who is accessing them or when they were last edited.
Also consider the implications of injecting RockMelt's drag-and-drop sharing style into this sort of Google App-optimized browser. Want to share a spreadsheet with a contact? Drag and drop it onto their image on the left. Want to turn an email into a Google Doc or perhaps a Word doc? Drag the email to the Documents icon. Want to preview a PDF or add it to your library? Drag and drop. Send a desktop file to a contact? Drag and drop it on their image, then choose whether you want to send it via email or over chat.
Conceivably, Google's forthcoming Chrome OS will enable the sort of heightened integration between browser and Google Apps, given that the company has telegraphed plans to eliminate the familiar icon-riddled desktop motif entirely. If not, though, RockMelt could serve as a promising model for another developer out there looking to groom a version of Chome for productivity use instead of social interaction.
RockMelt is free but, for now, requires an invitation to get a copy. You can request one via the RockMelt website or from a friend who already has it installed.
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