TopHeader div only front page

Can I easily hide the TopHeader div on all pages except the home page? That is, I'd like to let folks see all of the WordPress posts and pages regardless of their registered/logged in status. Buddypress would remain private, visible only to those registered members who are actually logged in.

In effect, when viewing Posts/Pages the only difference between logged-in users and not logged-in would be the salutation and Buddypress quick links from the OptionsBar div, which is only visible to logged-in users.