Erbil, Iraq — Heavily armed Islamic State militants currently surround the Syrian city of Kobane, also known as Ayn Al-Arab, from three sides; on the fourth lies the Turkish border. Inside the city, a 74-year-old Kurdish man named Uztas Osman waits with his rickety old Kalashnikov, ready to defend his hometown.

“He says he will stay ‘until ISIS comes next to my door,’” his anxious daughter, Sherin Sheihk Othman, tells me from her home in Erbil, Iraq, where she lives with her husband. She has the TV on constantly, Facebook open, and she’s calling her father several times an hour for updates.

The fight to defend Kobane has heated up this week as the Islamic State launched a major offensive against the city. Already in recent days, it has captured around 60 villages nearby. Meanwhile, a coalition of the United States and Arab forces has began a large-scale air campaign against the Islamic State in Syria, focusing its efforts in Raqqa and Aleppo, and along the Iraqi–Syrian border.

Many Kurds in the region want the United States and international forces to also provide air support to help the Kurdish forces and local militiamen preparing to defend Kobane, which is not only home to many Syrian Kurds; recently, the city has also served as a refuge for tens of thousands of Christians and Arabs.

But the battle of Kobane is not just a local matter. A shared border with Turkey gives it geopolitical importance. The Islamic State, The Economist reported this week, “sees the territory as strategic because it lies close to the edges of its ‘caliphate’ and to a supply route used by foreign fighters joining the group.”

Meanwhile, Kurds — like Osman, who worked for a long time as a judge in Kobane — view the battle in a bigger context. It’s not just a fight against the Islamic State, they believe; it’s also an opportunity to advance the cause of Kurdish independence.

Kobane is “a metric of the strength of the Kurds,” says Ilan Berman, vice president of the American Foreign Policy Council. “The narrative I’m seeing is that Kurds are looking at the fight against ISIS as a pivotal moment where the world will wake up, and it will alter the scales as to whether Kurdistan is feasible. Personally, I think [an independent] Kurdistan is probably not going to happen, but it’s clear [many Kurds are] seeing this as an opportunity to prove themselves, prove their military and political mettle.”

Today, hundreds of Kurdish men from Kobane have dropped their women and children off near the Turkish border, where as many as 130,000 now seek refuge, and then returned to fight, joined by Turkish Kurds.

Any successes the Kurdish troops gain will not be fully welcomed by Turkey, which remains uneasy after 30 years of fighting with Kurdish insurgents, a struggle that has claimed the lives of more than 40,000 people there. Some Kurds even believe that the Turkish government has been quietly helping the Islamic State, either directly or indirectly through inaction, because of its fear of strong and organized Kurdish forces.

“The fighting between Syrian Kurdish militiamen and Islamic State fighters in the town of Kobane exemplifies the strategic dilemma that Turkey faces in the Syrian conflict,” says Kamran Bokhari, an adviser for Middle Eastern and South Asian affairs at Stratfor, a geopolitical intelligence and advisory firm based in Texas. “Ankara does not want to see the Islamic State create a major jihadist sanctuary on its borders, and the main arrester in the path of [Islamic State] militants are the Syrian Kurds. At the same time, however, Turkey does not wish to see the Syrian Kurds gain an edge to where they embolden Turkey’s Kurdish separatists.”

While the Syrian Kurdish forces have thus far been the most successful in fighting the Islamic State in Syria, they lack international support, says Michael Rubin, a resident scholar at the American Enterprise Institute. These troops have been “effectively boycotted by Turkey, the United States, the Syrian regime, and, for that matter, a cynical Iraqi Kurdish leadership.”

Meanwhile, Rubin adds, the Islamic State has benefited from vast and sophisticated stocks of weapons captured as it won turf in Iraq. “Kobane is threatening to become the Kurds’ Stalingrad, a turning point in the war,” he says.

On Monday, the Wall Street Journal quoted a Turkish official who said clashes had occurred only about two miles outside the city, and “it is a matter of a day or two for Kobane to fall.” Yet overnight, that line held.

Back in Erbil, Sherin Sheihk Othman says she’s hearing conflicting accounts from her friends back home about whether ISIS has advanced or retreated. But the air strikes, though not in Kobane, have boosted the morale of those who stayed to fight, she says, adding that she remains cautiously optimistic.

“When you see the news, social media, you think [Kobane] is going to fall down [to ISIS],” she says. “But when I talk to people on the ground, I feel relief. . . . I have hope.”

— Jillian Kay Melchior is a Thomas L. Rhodes Fellow for the Franklin Center for Government and Public Integrity. She is also a Senior Fellow at the Independent Women’s Forum.