subscribe to public google calendars on iphone

Your question is asking us to write your app for you - no-one is going to do that for free so that's why your question is being voted down and getting no answers.
You need to be more specific and ask smaller questions. You're also going to need to specify more details i.e.

• Do you want to know how to show a list on an iPhone (hint: look at a UITableView)
• Do you want to know how to get a list of calendars from Google (hint: Google for 'Google calendar API')
• Do you want help connecting to calendars or just in showing the list of possible calendars?
• Will the list of calendars change or can you just hardcode it into the app?

This question's probably not going to get a real answer so I'd think more about what you want and ask another, smaller clearer question :)