Is it possible to add an eventlistener on a DIV?

Yeah, that's how you do it.

document.getElementById("div").addEventListener("touchstart", touchHandler, false);
document.getElementById("div").addEventListener("touchmove", touchHandler, false);
document.getElementById("div").addEventListener("touchend", touchHandler, false);

function touchHandler(e) {
  if (e.type == "touchstart") {
    alert("You touched the screen!");
  } else if (e.type == "touchmove") {
    alert("You moved your finger!");
  } else if (e.type == "touchend" || e.type == "touchcancel") {
    alert("You removed your finger from the screen!");
  }
}

Or with jQuery

$(function(){
  $("#div").bind("touchstart", function (event) {
    alert(event.touches.length);
  });
});