How to implement push notification cross-browser?

I have a web application and I need the user to be able to see wether a notification for them has landed. I want the notification icon to change it's state when they have a new one.

Basically, I want to listen when the API endpoint updates it's state for the current user and the front end to change it's state.

I thought of make that endpoint as an observable and the front end as an observer, but I don't know if that fits in what I need.

Any ideas?

via René Vidriales Trujillo