“These operations by Turkey are obviously more against the Kurds than Daesh,” said Mahmoud Othman, a prominent Iraqi Kurdish politician, using the Arabic acronym for the Islamic State. He added: “People are afraid now. People are really afraid of what could happen in the end.”  Drawing on history, Kurds see themselves as the playthings of world powers, used in proxy fights when it serves someone’s interest and then discarded.  The United States, on balance, has arguably been a great friend to the Kurds, coming to their aid after the Persian Gulf war in the early 1990s and helping to establish an autonomous region for them in Iraq, safe from Saddam Hussein’s brutality.  However, the United States also figures prominently in that historical memory of betrayal. In 1975, after the C.I.A. worked with Iran to supply weapons to the Kurds to fight Mr. Hussein’s regime, Secretary of State Henry A. Kissinger abruptly pulled the plug after a reconciliation between Tehran and Baghdad.  “In 1975, the same betrayal of the Kurds happened,” said Hasos Hard, a Kurdish journalist in northern Iraq, when asked about his reaction to the American support for Turkey’s Syria incursion.  Many analysts, though, as well as Syrian Kurdish fighters on the ground, say the accusations of betrayal are not quite right — at least not yet.  There is little sign that the United States has abandoned the Syrian Kurds. American officials have worked to negotiate a truce on the ground between the rebels backed by Turkey and the Kurdish militia, known as the People’s Protection Units, and fighting has calmed in recent days.  But many Kurds say they now see the writing on the wall and worry that once the Islamic State is driven from its capital in the Syrian city of Raqqa, the United States will sell them out.  Mr. Hiltermann said that when he traveled to northern Syria this year, he was asked this question, over and over, from the Kurds: “What do you think the Americans will do when Raqqa is taken?”  The question highlights the conundrum that the increasingly complicated Syrian battlefield presents the United States, which has tried to balance its relations with Turkey and the Syrian Kurds — a primary Turkish enemy because of their ties to militants inside the country.  Even though the United States has funneled weapons to the Syrian Kurds and provided them with military training, it has not established ties to the militia’s political wing, the Democratic Union Party, because of Turkish concerns. Nor has it promised them anything beyond military support in the fight against the Islamic State, other than expressions of support for a Kurdish role at the negotiating table when, or if, serious peace talks get underway.  Aliza Marcus, an author and expert on the Kurds, said, “it seems crass by the U.S.” to provide military support without any steps to establish political ties. This seems especially true now, she said, after the Kurds took heavy casualties in pushing the Islamic State out of Manbij, a city in northern Syria they recently liberated, and are now being asked to leave because Turkey does not want them there.  Lacking United States support, the Democratic Union Party has been shut out of Syrian peace talks that have been held in Geneva, and now there are increasing worries that Washington will eventually distance itself from the Syrian Kurds in a bid to improve relations with Turkey.  “The U.S. themselves, they say, these are the best fighters against Daesh,” said Mr. Othman, referring to the People’s Protection Units. “These are the best allies. Hopefully they will stick to that, and help them, and not leave them in the end.”  The recent events stand in marked contrast to a year ago, when it seemed that the Kurds were capitalizing on the turmoil in the Middle East to make historic gains. In Syria, they had secured land and found a powerful benefactor in the United States. In Turkey, for the first time, a Kurdish political party entered Parliament after elections. In Iraq, amid the fight against the Islamic State, they took control of Kirkuk, a city historically divided between Arabs and Kurds.  A year later, though, those prospects have dimmed. Iraq’s Kurds, somewhat insulated from the Syrian crisis, are pushing forward with their ambitions for independence, undaunted by an economic crisis. But in Turkey a decades-long war has resumed between the Kurdistan Workers’ Party and the Turkish state, and the main Kurdish political party has been isolated from national politics. In Syria, the Turkish military has quashed the Kurds’ efforts to link their two territories.  Further complicating matters, the Syrian conflict has become intertwined with Turkey’s domestic turmoil. Turkey now sees itself as fighting the Kurdistan Workers’ Party on three fronts: in Turkey, in northern Syria and in northern Iraq, where its members hide out in the mountains. As a result, analysts now say that there can be no final settlement of the Syrian civil war without the resumption of peace talks between Turkey and the Kurdistan Workers’ Party, of which the Democratic Union Party is its Syrian affiliate.  For now, the Kurds are still counting on the Americans to preserve them a place in a future Syrian state. “They should help them politically, to have rights in Syria,” Mr. Othman said. The Kurds, he said, “want a new Syria to be established, with them having a say in it.”  If nothing else, the American military support, even without any promises on the political front, has legitimized the Syrian Kurds’ ambitions. It has helped them to secure a large section of territory they say they will never give up, no matter what their patrons do.  “Throughout history, the Kurds were abandoned,” said Ahmad Haj Mansour, a Democratic Union Party official who lives in Britain. “But now, the time and place is different. We don’t need world powers to survive. We are in charge of our land, and we have fighters.”  Follow Tim Arango on Twitter @tarangoNYT.  Karam Shoumali contributed reporting from Istanbul, and Kamil Kakol from Sulaimaniya, Iraq.
Throughout history, Washington and other Western powers have used the Kurds for their ends, then abandoned them when it became expedient.