Of all the foreign problems facing prime minister-designate Justin Trudeau, the war in Syria and Iraq remains the most nettlesome.

It is tied to almost everything.

The Syrian refugee crisis that dominates headlines in Europe — and that made its way into the Canadian election campaign — is a direct result of that war.

Canada’s fraught relationship with Russian President Vladimir Putin over Ukraine is complicated by Moscow’s direct diplomatic and military involvement in Syria.

The North Atlantic Treaty Organization, Canada’s most important military alliance, is under strain because of Turkey’s position in this middle-eastern war.

As a NATO member, Turkey has the right to call on other members of the alliance when it acts to defend itself against foreign threats.

But in this war, the enemies Turkey has chosen to fight are Kurds based in Iraq and Syria who are also allies of NATO members like Canada and the United States in their battle against Islamic State militants.

Finally, and in spite of U.S. President Barack Obama’s reluctance, Canada’s most important ally and trading partner is being dragged willy-nilly into this war.

That point was underlined this week when an American commando was killed in Iraq after a joint U.S.-Kurdish attempt to free prisoners held in an Islamic State stronghold.

The American was not the first foreign military adviser killed in this war. Canadian Sgt. Andrew Doiron suffered the same fate earlier this year when his patrol was mistakenly fired on by friendly Kurdish troops.

Both deaths were a reminder that in the heat of battle, fine distinctions between training and combat can quickly become blurred.

Trudeau’s official position, as outlined in the Liberal party’s election platform, is that he will “end the combat mission in Iraq.”

But the Liberals defined the term “combat” narrowly to include only Canada’s participation in the air war over Syria and Iraq.

In the Commons, they always supported the Conservative government’s decision to send Canadian special forces troops to Iraq to take part in “training.”

The party platform promises to continue this, saying a Liberal government “will refocus Canada’s military contribution in the region on the training of local forces.”

Trudeau has said he explained his position to Obama and that the U.S. president understood.

I expect Obama did understand. I expect he was also not overly discomfited at Trudeau’s decision to pull out Canada’s six CF-18 jets from the air war. Canada’s role here was always minor.

What’s more important politically to Washington is that the U.S. not be the only Western country with at least some troops on the ground.

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The refugee crisis has increased pressure on Western nations to intervene more forcefully in the war.

The reason is not that Western leaders care that desperately about Syrian refugees. There was little pressure to act when these refugees stayed in Turkey, Jordan or their own country.

But now thousands of refugees are flooding into Europe, upsetting the delicate political and economic balance that had effectively erased most of the continent’s borders.

Borders are back with a vengeance, not just in anti-refugee nations like Hungary but in countries like Germany that have been more welcoming to foreigners.

Most leaders now seem to understand that the Syrian refugee crisis can be solved only by ending, or at least tamping down, the Syrian civil war.

The New York Times reports increased pressure on Obama to declare a no-fly zone over Eastern Syria in order to prevent more civilians from fleeing.

Meanwhile, Russia is hinting that Syrian dictator Bashar Assad may have become more amenable to a negotiated solution.

Regardless of what happens, the new Canadian government will find it difficult to stay aloof.

A U.S. no-fly zone would also require troops — and perhaps military advisers — on the ground in Syria to prevent the protected area from being used as a staging ground for rebel forces opposed to Assad. Otherwise American and Russian jets could find themselves in direct conflict.

To use Trudeau’s phrase, the Liberal election victory Monday means that Canada will no longer “whip out our CF-18s” in Iraq and Syria.

But is the combat mission really over? That’s less clear.

Thomas Walkom’s column appears Wednesday, Thursday and Saturday.

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