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:

   	<touchégg>
   	<settings>
   	<property name="composed_gestures_time">0</property>
   	</settings>
   	<application name="All">
   	<gesture type="DRAG" fingers="3" direction="RIGHT">
   	<action type="SEND_KEYS">Super+Right</action>
   	</gesture>
   	<gesture type="DRAG" fingers="5" direction="DOWN">
   	<action type="SEND_KEYS">Control+minus</action>
   	</gesture>
   	<gesture type="DRAG" fingers="5" direction="UP">
   	<action type="SEND_KEYS">Control+Shift+equal</action>
   	</gesture>
   	<gesture type="DRAG" fingers="3" direction="LEFT">
   	<action type="SEND_KEYS">Super+Left</action>
   	</gesture>
   	<gesture type="DRAG" fingers="3" direction="UP">
   	<action type="MAXIMIZE_RESTORE_WINDOW"></action>
   	</gesture>
   	<gesture type="DRAG" fingers="4" direction="UP">
   	<action type="SEND_KEYS">Super</action>
   	</gesture>
   	<gesture type="DRAG" fingers="4" direction="DOWN">
   	<action type="SEND_KEYS">Super+m</action>
   	</gesture>
   	<gesture type="TAP" fingers="3" direction="">
   	<action type="MOUSE_CLICK">BUTTON=2</action>
   	</gesture>
   	<gesture type="DRAG" fingers="3" direction="DOWN">
   	<action type="MINIMIZE_WINDOW"></action>
   	</gesture>
   	</application>
   	<application name="Evince">
   	<gesture type="DRAG" fingers="4" direction="LEFT">
   	<action type="SEND_KEYS">Control+Left</action>
   	</gesture>
   	<gesture type="DRAG" fingers="4" direction="RIGHT">
   	<action type="SEND_KEYS">Control+Right</action>
   	</gesture>
   	</application>
   	<application name="Firefox">
   	<gesture type="DRAG" fingers="4" direction="LEFT">
   	<action type="SEND_KEYS">Alt+Left</action>
   	</gesture>
   	<gesture type="DRAG" fingers="4" direction="RIGHT">
   	<action type="SEND_KEYS">Alt+Right</action>
   	</gesture>
   	</application>
   	<application name="Nuvola Player, nuvolaplayer">
   	<gesture type="DRAG" fingers="4" direction="LEFT">
   	<action type="SEND_KEYS">Alt+Shift+Left</action>
   	</gesture>
   	<gesture type="DRAG" fingers="4" direction="RIGHT">
   	<action type="SEND_KEYS">Alt+Shift+Right</action>
   	</gesture>
   	</application>
   	</touchégg>

   view raw touchegg.conf.xml hosted with ❤ by GitHub

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.