display a slider outside of subdomain folder wp

In a normal WP flow following happens:

1. Web server get request for pretty permalink (typically) and sends it to index.php of WP installation.
2. WP core loads and displays a page, respective to that input.

In your case the root of the site points to something different entirely. So there is no WP core load happening.

You could integrate WP into your home page (assuming it is also PHP at least). For that you would have to:

1. Load WP core yourself (wp-load.php and around).
2. Figure out how to retrieve data or run functionality you need, without “normal” process of turning URL into page output.