Europe\'s main stock markets advanced on Tuesday in cautious deals as investors awaited the outcome of the US presidential election and digested news of bumper profits from carmaker BMW. Markets held on to their gains despite a downbeat survey which showed that private sector business activity across the eurozone shrank at its fastest rate in three-and-a-half years in October. London\'s FTSE 100 index of major blue-chip companies won 0.53 percent to 5,870.32 points in late morning deals, Frankfurt\'s DAX 30 added 0.70 percent to 7,377.19 points and in Paris the CAC 40 gained 0.73 percent to 3,474.10. In foreign exchange activity, the euro sank to $1.2764 -- the lowest level since September 11 -- weighed down by concerns over debt-plagued Greece, and as the dollar attracted safe-haven demand amid US election uncertainty. The European single currency later stood at $1.2797, up from $1.2791 late in New York on Monday. Gold prices rose to $1,690.57 an ounce on the London Bullion Market from $1,683.50 Monday. US polling stations opened on Tuesday, with Democratic incumbent Barack Obama and Republican challenger Mitt Romney neck-and-neck, leaving markets trading in a narrow band as investors held off making any bets until the outcome is known. \"Stock markets are higher in Europe this morning, but there is an element of caution ahead of the presidential election tonight,\" said analyst Craig Erlam at trading group Alpari UK. \"There is still nothing in it between the two parties, which is only building on the uncertainty we\'re currently seeing in the markets. \"One thing does look certain now and that is no matter which candidate wins, the parties are going to have to come to some agreement on how to overcome the fiscal cliff.\" Warnings are mounting about the dangers of the US fiscal cliff -- a mandated sharp cut in government spending and the end to a package of tax breaks expected to suck half a trillion dollars out of the economy next year. IMF chief Christine Lagarde on Monday urged the United States to \"address quickly\" the budget mess facing the government, no matter who wins the election. \"Equities are marginally higher this morning as investors follow the US election,\" said Mike McCudden, head of derivatives at online stockbroker Interactive Investor. \"Regardless of the US election outcome, resolving the \'fiscal cliff\' situation will dominate the agenda in the weeks ahead, with the ensuing volatility forcing many investors on to the sidelines.\" US Polls opened at 6:00 am (1100 GMT) in battleground states New Hampshire and Virginia, as well as New York, New Jersey, Connecticut, Indiana, Kentucky, Maine and Vermont. Back in Europe, investors set aside news of shrinking eurozone private sector business activity to focus on healthy earnings from German luxury carmaker BMW. The automaker said its net profit jumped 16 percent to 1.289 billion euros ($1.6 billion) in the three months from July to September, while revenues soared 13.7 percent to 18.817 billion euros. BMW also stuck to its forecast for record sales and earnings this year. Asian stock markets closed mixed on Tuesday as investors also awaited the start of this week\'s Communist Party\'s 18th congress, which will see a once-in-a-decade leadership transition in China. Hong Kong slipped 0.28 percent, Shanghai shed 0.38 percent and Tokyo softened 0.36 percent, while Seoul rose 1.05 percent and Sydney closed 0.24-percent higher.