The debates are done: Three face-offs between Mitt Romney and President Obama, totaling 41 / 2 hours and combined transcripts of more than 50,000 words, longer than “The Great Gatsby.” But this was a novel with some glaring plot holes.

There were a startling range of issues that were never broached, a list that includes climate change, housing policy and appointments to the Federal Reserve. But one topic stands out for the mismatch between how much it has affected the economy — and how much of Obama’s time and energy it has claimed — relative to its nonexistence in the debates.

Europe’s financial woes have weighed on U.S. economic growth — driving down earnings among American companies that do business there and walloping financial markets on both sides of the Atlantic — amid persistent worries that the euro currency could unravel. It is impossible to know what the U.S. economy would have done over the past three years absent a fiscal crisis in Greece and other European countries (or if Germany and other financially stronger nations on the continent had responded to that crisis crisply and decisively). But it is easy to imagine that this was the difference between steady emergence from the nation’s deep doldrums and the muddling along that has occurred.

So, on this slow-moving crisis that has persisted for most of Obama’s term, what has he done about it? Obama hasn’t boasted about his record, and Romney hasn’t attacked it (and none of the three moderators asked about it). Here is a sense of what the Obama administration has been doing in Europe and some possible critiques of that performance:

Treasury secretary’s role

Treasury Secretary Timothy F. Geithner has been the administration official taking the lead on the euro-zone crisis, and his background made him a good match for the moment. He was a veteran of addressing fiscal crises in East Asia and elsewhere in the 1990s and had become a member of the close-knit club of global central bankers during his time as president of the New York Fed from 2003 to 2009. He has used that background to serve as a sounding board and strategic influencer of the different parties in Europe.

His past has given him the ability to speak with the top leaders of the European Central Bank and International Monetary Fund, and finance ministries in Germany, France, Greece or elsewhere, and help them identify common ground and areas for compromise in often-difficult negotiations. His overarching stance, European officials have said, is generally not to advocate for any specific crisis response, but to be a force steering the conversation toward bolder, more aggressive stances.

In one much-reported example, in May 2010 European leaders were discussing an early version of what would become a Europe-wide stability fund. They were talking about something on the order of 100 billion euros, and Geithner convinced them that markets would scoff at such a sum and that it needed to be about 1 trillion euros.

President’s influence

Obama has stepped in regularly to apply pressure. He has maintained a particularly good bond with German Chancellor Angela Merkel, European sources have said, and has used private diplomacy to try to persuade Germany to deploy more of its financial resources toward addressing the crisis.

One important moment when Obama’s influence played a role was a Group of 20 summit in Cannes, France, in November 2011. Silvio Berlusconi, then the Italian prime minister, was dragging his heels on implementing structural changes that were the price to be paid for financial help from the rest of Europe. The scandal-tarred leader had lost all credibility with other European officials. Obama, Merkel and then-French President Nicolas Sarkozy essentially ganged up on Berlusconi, twisting his arm to accept monitoring of Italian financing by the IMF. That set in place events that led to Berlusconi’s resignation and more credible Italian leadership coming to power, namely Prime Minister Mario Monti.

“Having heard from our European partners over the past two days, I am confident that Europe has the capacity to meet this challenge,” Obama said after the Cannes summit, giving officials there a to-do list that included “a credible fire wall to prevent the crisis from spreading, strengthening European banks, charting a sustainable path for Greece, and confronting the structural issues that are at the heart of the current crisis.”

Although the Obama administration has been able to influence events in Europe, the IMF has been its most significant and direct channel for influence. The United States is the largest shareholder of the IMF (though it is far from a majority, at 17 percent).

Early on, Europe was torn on whether to bring in the IMF to help Greece and other troubled nations; a particular objection of Sarkozy was that doing so would give the Americans a lever of power over Europe. Ultimately, Merkel and other officials judged that they needed the IMF’s technical expertise and experience in restructuring of government finances, and extra financial contribution from the world community was attractive as well. The Obama administration supported this IMF involvement but was wary of anything that would make the fund — and the American taxpayer — a primary driver of the crisis response. The administration’s logic has been that the euro zone is a wealthy group of countries with, in the aggregate, sound finances; the challenge is to help the different actors make the sacrifices they need to prevent an implosion of the currency.

Critiques and challenges

So, what are the critiques of the administration’s stance toward Europe? One would be the simplest: That it hasn’t worked. The quiet, subtle diplomacy of Obama and Geithner hasn’t led to an overarching, permanent solution to the imbalances within the 17-nation euro zone. Perhaps a more adept application of U.S. influence would have led to a better place.

But the challenge for critics, including any attack that Romney might level, is to identify how it could have been better. If Obama and Geithner had been louder and more accusatory in their criticism of Europe’s handling of the situation, it could have backfired and offended European sensibilities, making the United States less influential. Indeed, that is what happened with Britain; some European officials have become dismissive of advice from British leaders, seeing them as meddling in affairs on the continent that are not their business.

The United States could have had a more direct seat at the table if it had offered major financial resources to help solve the problem, either through the IMF or on its own. But it is hard to imagine that any political leader, Republican or Democratic, seeing financial assistance to Europe amid a U.S. recession as a wise idea.

This tension shows why Romney hasn’t made Europe a campaign issue: It’s not easy to sum up a succinct criticism of Obama’s handling of Europe, only to criticize the outcome as inadequate. And that has far more to do with decisions by German and French and Greek and Italian and Spanish officials than anyone at 1500 or 1600 Pennsylvania Ave.

Still, these questions are important enough that it would have been nice for them to be aired during the debates. Europe’s future is a bigger deal than Big Bird or binders full of women.