Having a duplicate homepage is a major issue, you should redirect any duplicate home pages so you only have one. The reasons for this are to consolidate link juice and also stop the duplication of the content on the homepage. You need to redirect www. urls to the root or vis versa, this is simple to do on a WordPress theme or in your c/panel or ftp. Now when you have a url with yoursite.com/index.html it becomes a a whole different kettle of fish. If you simply 301 redirect yoursite/index.html to the root you will cause a continual loop. Here is how to redirect yoursite.com/index.html to your root domain without causing a constant loop for search engines.
So here is how to redirect index.html to the root
In your .htaccess folder insert the following code
# redirect html pages to the root domain
RewriteRule ^index\.html$ / [NC,R,L]
You can use the following code below to redirect all the index.html urls to their roots.
RewriteRule ^index\.html$ / [R=301,L]
RewriteRule ^(.*)/index\.html$ /$1/ [R=301,L]