1. Install the linux-xps13-archlinux kernel (now in the AUR)

   Note: Since I wrote this, it’s possible that the patched kernel now has more features than only touchpad support.

2. Install xf86-input-synaptics and, from AUR, touchegg and touchegg-gce-git (this last one is to be able to configure gestures with the graphic interface).

3. Edit /etc/X11/xorg.conf.d/50-synaptics.conf

   Section "InputClass"
           Identifier "touchpad catchall"
           Driver "synaptics"
           MatchIsTouchpad "on"
           Option "TapButton1" "1"
           Option "TapButton2" "0"
           Option "TapButton3" "0"
           Option "ClickFinger2" "0"
           Option "ClickFinger3" "0"
   
   
   # This option is recommend on all Linux systems using evdev, but cannot be
   # enabled by default. See the following link for details:
   # http://who-t.blogspot.com/2010/11/how-to-meta:ignore-configuration-errors.html
           MatchDevicePath "/dev/input/event*"
   
   
   EndSection
   

4. Configure your gestures with Touchègg

   Here's my ~/.config/touchegg/touchegg.conf:

5. Add to your session (using gnome-session-properties for instance):

   • touchegg

The real improvement is that I can use three-finger tapping to simulate the middle-click mouse button which is used for quick pasting or for opening links in a new tab.

As far as "pinching" is concerned, it does not work reliably at all for me.