Gmail doesn't recognize dots (.) as characters within a username. Google Ignores "." in Google account username at time of login and time of creating new account. This way, you can add and remove dots to your username and change your e-mail id. May be some of you do not believe, but this is a very interesting Fact.
It doesn't matter whether you have created your Google e-mail address with or without dots. You can still login and access your account without worrying about dots.
Also, Gmail user names are case insensitive, so it doesn't matter if you enter upper case or lower case letters. Few e-mail IDs shown below would work as same for representing a single Google e-mail address.
Any e-mail send to anyone of the above e-mail ID will be delivered to the same inbox, since the characters in the username are the same. You can see this if you try to sign in with your username, but adding or removing a dot from it. You'll still go to your account.
Important to mention that hyphens (-) and underscores (_) can't be used in a Gmail address. Different from Google e-mail (Gmail), Google Apps does recognize dots.
Check this and tell whether it works for you?