Deploying Single Page Apps on Github Pages is fine if your app never navigates away from you index.html
However, if you have a more complex app and have /about or /user/21, Gihub Pages will fail. Here's the fix I usually use, that I found in a github repo some time ago:
There are two steps:

In the <b>&lt;head&gt</b> section of your <b>index.html</b>, just before <b>&lt;/head&gt;</b> closing tag, which usually resides in you <b>/public</b> folder add the following:

[code]

  <script type="text/javascript">
    // Single Page Apps for GitHub Pages
    // https://github.com/rafrex/spa-github-pages
    // Copyright (c) 2016 Rafael Pedicini, licensed under the MIT License
    // ----------------------------------------------------------------------
    // This script checks to see if a redirect is present in the query string
    // and converts it back into the correct url and adds it to the
    // browser's history using window.history.replaceState(...),
    // which won't cause the browser to attempt to load the new url.
    // When the single page app is loaded further down in this file,
    // the correct url will be waiting in the browser's history for
    // the single page app to route accordingly.
    (function(l) {
      if (l.search) {
        var q = {};
        l.search.slice(1).split('&').forEach(function(v) {
          var a = v.split('=');
          q[a[0]] = a.slice(1).join('=').replace(/~and~/g, '&');
        });
        if (q.p !== undefined) {
          window.history.replaceState(null, null,
            l.pathname.slice(0, -1) + (q.p || '') +
            (q.q ? ('?' + q.q) : '') +
            l.hash
          );
        }
      }
    }(window.location))
  </script>

[/code]


In the same <b>/public</b> folder create a <b>404.html</b> file and add the following content to it:

[code]
<!DOCTYPE html>
<html>
  <head>
    <meta charset="utf-8">
    <title>Single Page Apps for GitHub Pages</title>
    <script type="text/javascript">
      // Single Page Apps for GitHub Pages
      // https://github.com/rafrex/spa-github-pages
      // Copyright (c) 2016 Rafael Pedicini, licensed under the MIT License
      // ----------------------------------------------------------------------
      // This script takes the current url and converts the path and query
      // string into just a query string, and then redirects the browser
      // to the new url with only a query string and hash fragment,
      // e.g. http://www.foo.tld/one/two?a=b&c=d#qwe, becomes
      // http://www.foo.tld/?p=/one/two&q=a=b~and~c=d#qwe
      // Note: this 404.html file must be at least 512 bytes for it to work
      // with Internet Explorer (it is currently > 512 bytes)

      // If you're creating a Project Pages site and NOT using a custom domain,
      // then set segmentCount to 1 (enterprise users may need to set it to > 1).
      // This way the code will only replace the route part of the path, and not
      // the real directory in which the app resides, for example:
      // https://username.github.io/repo-name/one/two?a=b&c=d#qwe becomes
      // https://username.github.io/repo-name/?p=/one/two&q=a=b~and~c=d#qwe
      // Otherwise, leave segmentCount as 0.
      var segmentCount = 0;

      var l = window.location;
      l.replace(
        l.protocol + '//' + l.hostname + (l.port ? ':' + l.port : '') +
        l.pathname.split('/').slice(0, 1 + segmentCount).join('/') + '/?p=/' +
        l.pathname.slice(1).split('/').slice(segmentCount).join('/').replace(/&/g, '~and~') +
        (l.search ? '&q=' + l.search.slice(1).replace(/&/g, '~and~') : '') +
        l.hash
      );

    </script>
  </head>
  <body>
  </body>
</html>
[/code]

Please pay attention to <b>segmentCount</b> if you're NOT using a custom domain as it may need changed to 1. 

Many thanks to Rafael for this!