Activity in China’s manufacturing sector unexpectedly picked up in September even as factory employment slumped to a 5-1/2-year low, a survey showed on Tuesday, a potential source of worry for Communist leaders who prize social stability above all else. The HSBC/Markit Flash China Purchasing Managers’ Index (PMI) rose to 50.5 in September from August’s final reading of 50.2. A hefty drop in employment could raise alarm bells for the Chinese government, which has indicated it will tolerate slower economic growth as long as employment is not affected.