NEW YORK — Stock indexes rose, fell, rose back again and then ended the day more or less where they started. As they have been doing for weeks now, traders remain focused on the latest hope for a resolution to Europe’s debt crisis — this time, a weekend summit of European leaders.

The Dow Jones industrial average moved between gains and losses all day before ending up 37.16 points, or 0.3 percent, to close at 11,541.78. The Dow had been down as many as 113 points shortly after noon. The Dow is 0.3 percent below where it started the year, and is headed for its first down week after three weeks of gains.

Trading was choppy as talks across the Atlantic appeared to falter because of differences between Germany and France over how to protect European banks from the consequences of a default by the Greek government. Later in the day stocks rose slightly on news that a second summit meeting would take place next week after it became clear that France and Germany would not be able to bridge their difference in time for the meeting Sunday.

A messy default by Greece could lead to deep losses for European banks that hold Greek debt. If that leads them to pull back on lending to each other, it could cause another freeze in global credit markets like the one in late 2008 after Lehman Brothers collapsed.

The Standard & Poor’s 500 index rose 5.51 points, or 0.5 percent, to 1,215.39.