November 12, 2015 11:11 AM EST

Sinjar, the focus of a major battle between Kurds and the Islamic State in Iraq and Greater Syria (ISIS) is critical both as a symbol and as a strategic point in the larger conflict with ISIS in Iraq and Syria.

The town lies on the main highway connecting two cities that are pillars of ISIS’ hold on large swaths of territory: Raqqa in Syria and Mosul in Iraq. Retaking the town would sever one of the group’s key supply lines and leave both cities vulnerable to attack from Syrian Kurds and the Iraqi army and militias.

Sinjar also has immense symbolic value. The ISIS fighters’ conquest of the town in August 2014 displaced tens of thousands of people, primarily from the Yezidi community. At one point, some 40,000 people were stranded on a mountain, facing violent death if they descended, or starvation if they stayed. They were later rescued by Kurdish fighters from neighboring Syria.

ISIS also abducted many of the more than 5,000 Yezidi women, turning many of them into slaves. Many Yezidi women have described how they were raped and abused.

Now, Kurdish forces say they are advancing in a campaign to retake the town, branded Operation Free Sinjar. They are backed by the air power of the U.S.-led coalition, which struck ISIS positions in the town overnight.

The autonomous Kurdistan Regional Government in northern Iraq said in a statement that the operation will include 7,500 of its Peshmerga fighters. They plan to cordon off the city, cut ISIS’ supply routes and “establish a significant buffer zone to protect the city and its inhabitants from incoming artillery.”

In addition to the Peshmerga, fighters loyal to the Kurdistan Workers Party, or PKK, are participating in the offensive, according to Reuters. The PKK is a Marxist Kurdish nationalist guerilla organization that has fought a long war with the government in neighboring Turkey.

The PKK is considered a terrorist group by Turkey and the U.S., but its branches in Iraq and Syria are now central to the U.S.-backed campaign against ISIS.

Although they are fighting the same battles, a rivalry exists between the Kurdistan Regional Government and the PKK and its local branches. Some Yezidis blamed the Peshmerga for failing to protect them during the battle of Sinjar. According to multiple reports, it was fighters from the People’s Protection Units, a PKK offshoot from Syira, who ultimately broke the siege and provided the stranded Yezidis safe passage.

According to Reuters, a PKK-trained Yezidi militia is also taking part in current offensive to recapture Sinjar.

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