The defeat of ISIS in the northern Syrian town of Kobani last January brought Kurdish fighters well-deserved international recognition. Not only was their victory strategic, but it also struck a blow to ISIS’s image as an unstoppable force in its quest to create an Islamic state. U.S. airstrikes assisted in the battle, but credit for the success belongs to the Kurds of Syria and Turkey, aided by 150 Peshmerga from Iraqi Kurdistan (KRG).

By most accounts, the Syrian Kurds—the People’s Protection Units (YPG)—and their counterparts from Turkey, the Kurdistan Workers' Party (PKK), have been the most effective forces against ISIS. But the West is hesitant to militarily contribute anything to them beyond air support, despite repeated calls from the Kurds for arms. Instead, the U.S. has funneled weapons toward moderate Syrian opposition rebels. To bolster these forces, the U.S. and Turkish governments will soon begin implementing a plan to train and equip 5,000 fighters a year for three years—though neither government can agree whether the real enemy is ISIS or Syrian President Bashar Al Assad.

So why hasn't the U.S.-led coalition armed the YPG, given their ability and willingness to confront ISIS? Most analysts agree that Turkey is the biggest obstacle. Joshua Landis, an expert on Syria and professor at the University of Oklahoma, said in an email that U.S. hesitation to arm the Kurds stems from their “connection to the PKK and a desire not to alienate the Turks more than necessary.” Greater Kurdish autonomy in Rojava—the three Kurdish-majority regions in northern Syria—could further embolden the Kurdish rights movement within Turkey’s borders.

Aaron Stein, an associate fellow at the Royal United Services Institute and an expert on Turkey, emphasized this point. “We aren’t arming [the Kurds] because we still take some of our cues from the Turkish government,” he said. The fact that the U.S. is even offering air support to the YPG is a “big deal,” according to Stein. “The airstrikes are a drastic change from what we used to do. It’s a fantastic change from our old policy. … It did not go over well in Ankara.”

The U.S. and Turkey, which is a NATO ally, still view the PKK—which has fought the Turkish state in a bloody insurgency for some three decades—as a terrorist group, even though the group declared a unilateral ceasefire in 2013 and is currently engaging in peace talks with the government. And the YPG in Syria are closely tied ideologically and operationally to the PKK. “They are linked through the supranational structure to the PKK. … And you have PKK embedded with them quite closely,” Stein said. The legal issue of arming a group on the U.S. State Department list of Foreign Terrorist Organizations (FTOs)—where the PKK, not the YPG, is listed—is also deterring lethal aid to the Kurds. But the U.S. only just removed the two dominant political parties in Iraqi Kurdistan from the list of terrorist groups in December, despite having been allies for the last decade. Some are calling for the delisting of the PKK as well.

Another concern in the West is that Syrian Kurds could gain control of new territories where they don't constitute an ethnic majority. “Many U.S. military analysts warn not to arm up the Peshmerga too much or Kirkuk and other hotspots of mixed ethnicity will be overrun by Kurds, causing greater problems down the road. The same logic goes for Syria,” Landis said. “The Kurds can take back Kurdish regions, such as Kobani, which ISIS took over, but they should not be used to extend Kurdish rule beyond the traditional Kurdish towns.”

“Such an obvious thing to do would be to bolster the YPG with more air activity,” said Jeff White, a defense fellow at the Washington Institute for Near East Policy. While the U.S. has continued to support the YPG with airstrikes, White believes that the absense of deeper U.S. involvement is a product of the Obama administration’s “conservative, traditional military strategy against ISIS.” It could also be related to the fact that, besides the battle of Kobani, the focus of operations against ISIS have been in Iraq. “Syria just isn’t seen as a major front against ISIS,” White said.

While there have been repeated calls to do more for the Peshmerga of northern Iraq, many prominent voices on the left are now calling attention to the military and political situation of Kurds in Rojava. The political wing of the YPG, the PYD, has been implementing radical democratic initiatives in the region since Assad's forces largely withdrew in 2012, including grassroots councils, women's organizations, and economic cooperatives. Anthropologist David Graeber, known for his role in the Occupy movement, visited the region last year and wrote a piece in The Guardian to call attention to their plight and the political and social institutions they've created (Graeber called Rojava “one of the world’s great democratic experiments.”). British journalist Owen Jones recently did the same. And Mehdi Hassan—generally on the anti-war left—was even more explicit, directly calling for military support. Backing the Syrian Kurds is thus one way to bolster the broader campaign against ISIS, with broad support across the political spectrum internationally.

Besides the need for arms, authorities in Rojava are also calling on Turkey to end its blockade of the region and open up humanitarian corridors to the three non-contiguous cantons (a word used as by the Kurds as a nod to the Swiss model of confederated states). So far, Turkey’s vehement opposition to a Kurdish-controlled Rojava is preventing even the most basic aid from getting in. “Make no mistake about: The Turks are terrified of Rojava,” Stein said. But even if the U.S. decides against direct military support, it should at least push for the opening of corridors from Turkey into the Kurdish cantons, particularly given how crucial a role it played in their creation. After all, it is possible Rojava's cantons would have been overrun by ISIS without the U.S. airstrikes. As Stein points out, U.S. airstrikes have already created the Kobani canton. “We are going to create Rojava.”