On August 24th, 2016, the Turkish military entered Syria near Jarabulus directly, together with various rebel groups. Jarabulus had been attacked with artillery and aircraft for severals days prior to this. As Turkey entered, the city was abandoned by IS and taken over without resistance. The same day the Jarabulus Military Council (JMC, part of SDF) marched North in direction of Jarabulus. The JMC went as far North as Amarinah, these former IS territories were abandoned too1.https://twitter.com/archicivilians/status/768512869075943424, which explains the rapid advance. Already on the 24th fighting between the SDF and the Turkish alliance started in Ayn Al-Bada.2.https://twitter.com/Syria_Rebel_Obs/status/768551394349555712
Between the 26th and the 29th SDF forces were driven south of the Sajur river, basically restoring their position pre-Turkish intervention. After the SDF was driven south of the Sajur river, talks about a ceasefire began to surface. Turkey denied that they entered a ceasefire, but fighting between SDF and the Turkish alliance mostly ceased.3.http://www.al-monitor.com/pulse/originals/2016/09/turkey-syria-turkish-kurdish-problem-deepens.html
After the SDF-Turkey fighting died down Turkish backed rebel forces went west of Jarabulus along the Turkish-Syrian border.4.https://twitter.com/ragipsoylu/status/770617009809809408 The rebels in the Azaz pocket, together with the support of Turkish tanks went east and took Al-Rai. On 4th September, Turkish backed rebels united both pushes and took the entire stretch of border between Jarabulus and Azaz.5.http://www.aljazeera.com/news/2016/09/syria-war-isil-driven-turkey-syria-border-160904164425932.html Meanwhile, SDF units in Afrin seized some IS villages east of their position.6.https://twitter.com/DrPartizan_/status/770692312217321472,7.http://aranews.net/2016/08/syrian-democratic-forces-launch-new-operation-isis-aleppo-expel-militants-four-villages/ This time the territory wasn’t abandoned by IS and fighting happened. The fighting inflicted casualties but didn’t reverse IS territorial loss.8.http://english.alarabiya.net/en/News/middle-east/2016/09/03/Turkey-pushes-west-in-offensive-against-ISIS-in-Syria.html
Following that, there was a long period of fighting between IS and the Turkish alliance as well as between IS and the SDF. The rebels together with Turkish support pushed South and created a pretty big pocket of IS territory. They moved to take IS territory to the South on two axis. One direction is in the East of the Aleppo countryside, taking Qantarah, Mirza and Tell Ali.9.https://twitter.com/CivilWarMap/status/773850860531089408 The other axis is South of Al-Rai where they took Wuquf, Qabasin, and eventually advanced to al-Bab. Turkey lost several tanks since their intervention, to both the SDF and IS.10.https://www.facebook.com/cagdasgundem10/videos/528996150619637/, 11.https://www.youtube.com/watch?v=DCCju3WOOYY
The front between the SDF and the Turkish alliance is pretty quiet, but there have been talks about Turkish backed rebels declaring the territory around Al-Bab a military zone and preparing for an offensive towards Manbij. 12.https://twitter.com/Terror_Monitor/status/773275251752865792, 13.https://twitter.com/QalaatAlMudiq/status/773416132787208193This would make it impossible for the SDF to connect the cantons once and for all.