This snippet maps mouse events and touch events onto one single event. This makes it easier in the code since you have to listen to only one event regardles whether it's desktop or mobile.

touchmouse.js

(function() {
    
    /* == GLOBAL DECLERATIONS == */
    TouchMouseEvent = {
        DOWN: "touchmousedown",
        UP: "touchmouseup",
        MOVE: "touchmousemove"
    }
   
    /* == EVENT LISTENERS == */
    var onMouseEvent = function(event) {
        var type;
        
        switch (event.type) {
            case "mousedown": type = TouchMouseEvent.DOWN; break;
            case "mouseup":   type = TouchMouseEvent.UP;   break;
            case "mousemove": type = TouchMouseEvent.MOVE; break;
            default: 
                return;
        }
        
        var touchMouseEvent = normalizeEvent(type, event, event.pageX, event.pageY);      
        $(event.target).trigger(touchMouseEvent); 
    }
    
    var onTouchEvent = function(event) {
        var type;
        
        switch (event.type) {
            case "touchstart": type = TouchMouseEvent.DOWN; break;
            case "touchend":   type = TouchMouseEvent.UP;   break;
            case "touchmove":  type = TouchMouseEvent.MOVE; break;
            default: 
                return;
        }
        
        var touch = event.originalEvent.touches[0];
        var touchMouseEvent;
        
        if (type == TouchMouseEvent.UP) 
            touchMouseEvent = normalizeEvent(type, event, null, null);
        else 
            touchMouseEvent = normalizeEvent(type, event, touch.pageX, touch.pageY);
        
        $(event.target).trigger(touchMouseEvent); 
    }
    
    /* == NORMALIZE == */
    var normalizeEvent = function(type, original, x, y) {
        return $.Event(type, {
            pageX: x,
            pageY: y,
            originalEvent: original
        });
    }
    
    /* == LISTEN TO ORIGINAL EVENT == */
    var jQueryDocument = $(document);
   
    if ("ontouchstart" in window) {
        jQueryDocument.on("touchstart", onTouchEvent);
        jQueryDocument.on("touchmove", onTouchEvent);
        jQueryDocument.on("touchend", onTouchEvent); 
    } else {
        jQueryDocument.on("mousedown", onMouseEvent);
        jQueryDocument.on("mouseup", onMouseEvent);
        jQueryDocument.on("mousemove", onMouseEvent);
    }
    
})();