There many Chrome extensions available on Chrome Web store that shows Google+ notifications when you’re signed into your Google account, even Google shows these  notifications to you. Google released Google+ Notifications Chrome extension for Chrome users which is available for download Chrome web Store.

official Google plus notifications extension for Chrome

If your Google+ account have one or more  notifications, notification icon on Chrome toolbar turns red click on it to view most recent notifications in drop down manner, you can click on “view all notifications” to see notifications on Google+. You need to signed into your Google account to see these notifications.

“See what’s happening on Google+ with the Google+ Notifications extension.

Whenever you have a new notification (for example, when someone adds you to a circle or shares a post with you), the extension button will turn red and show you how many updates are waiting for you. Once you click the button, a window will drop down showing you all of your most recent notifications. You can act on notifications right from the extension, whether you’re replying to a comment or adding someone back to your circles. That way you can stay up-to-speed with your circles on Google+ no matter where you are on the web” extension page describes.