Global stock markets opened a risk-filled new year still smarting from a rough 2011, as many exchanges remained closed. German and French stocks rose in light volumes as a a reading of manufacturing activity in Europe improved. Germany’s DAX closed up 3 percent Monday at 6,075 while the French CAC-40, which ended 2011 17 percent lower, climbed 2 percent to 3,222. Stocks fell in South Korea and closed flat in Taiwan. Trading was light with the New York, London and most Asian stock exchanges closed. Investors appeared to be reassured by European purchasing managers survey index numbers that improved in December from November. Activity in the manufacturing sector was up, but at levels that still show a fifth straight month of contraction. Many of the world’s leading indexes are coming off a down year. Britain’s FTSE was off 5.6 percent by year end, Japan’s Nikkei fell 17 percent to its lowest close since 1982, and the Standard & Poor’s 500 showed zero gain. Data releases later in the week such as euro zone inflation on Wednesday and German factory orders and US non-farm payrolls on Friday will give traders more grist. The US employment figure is expected to rise by some 150,000 after increasing 120,000 in November. Markets face an uncertain first quarter as euro zone leaders try to get control of government debt woes that threaten to harm the global economy with another financial meltdown. Much of the attention in coming weeks will center on Italy, the eurozone’s third-largest economy and the focal point of the eurozone’s struggle to deal with a crisis caused by heavy levels of government debt. Fears of default on those debts mean that bond investors demand ever-higher interest, making it a challenge for the new government of Prime Minister Mario Monti to roll over 53 billion euros ($69 billion) in debt maturing in the first quarter. If a country can no longer borrow affordably to pay off bonds that are maturing, it faces eventual default or a bailout. Debt woes may be compounded by at least a mild recession over the last quarter of 2011 and the first part of 2012. In Asia, South Korea’s Kospi, which lost 11 percent of its value last year, closed nearly unchanged at 1,826.37. South Korea’s tech sector move higher, with Samsung Electronics up 2.1 percent and LG Electronics gaining 2.3 percent. Steel giant POSCO slid 1.1 percent and Korea Electric Power shed 1.8 percent. Taiwan’s TAIEX, which was also open for business Monday, fell 1.7 percent to 6,952.21. Foxconn Technology, the world’s biggest contract electronics manufacturer, which makes iPads and iPhones for Apple Inc., fell 0.9 percent. Personal computer maker Acer Inc. shed 2.3 percent. The Asian-Pacific region’s major benchmarks, including Japan’s Nikkei 225 index, Hong Kong’s Hang Seng Index and Australia’s S&P ASX 200, were closed. Last year was one that traders would prefer to forget: most Asian equity indexes closed out 2011 deeply in the red. The Nikkei in Tokyo ended the year at 8,429.45 — its lowest closing since 1982. China’s benchmark Shanghai Composite Index, closed Monday, endured a 21 percent loss for the year as the impact of Beijing’s multibillion-dollar stimulus faded and the government tightened curbs on lending and investment to cool blistering economic growth.