I'm wondering the same, Mrs F; mine's flopped, so thinking of cutting it right back . .

I have one I am going to divide, but it is the deciduous type, so I am waiting until it dies back.

I have just Googled 'agapanthus care' and learnt that they can be left in the ground, they prefer a sunny position, and can be divided with equanimity!

Sheilabub's right - IF, that is, your variety of Agapanthus is a hardy one - not all are and may need winter protection in a cool greenhouse or similar.