Do the edges curl if laid as a rug on concrete?

It might if you leave the piece completely loose on the concrete. We always recommend to somehow secure the grass into the solid surfaces regardless a permanent or temporary applications before any usages. For permanent installations of turf onto concrete surface, you will need to use turf flies and 1/4” trowel and you need to make sure all edges have full contact with both glue and turf and concrete. For temporary installation, we recommend you to use strong double sided carpet tapes or Velcro along the edges to avoid any tripping hazards.