What is the full name of the person whose forces were unable to help in the assault against the Song?
The Mongols were allied with the Song, but this alliance was broken when the Song recaptured the former imperial capitals of Kaifeng, Luoyang, and Chang'an at the collapse of the Jin dynasty. The Mongol leader Möngke Khan led a campaign against the Song in 1259 but died on August 11 during the Siege of Diaoyu Castle in Chongqing. Möngke's death and the ensuing succession crisis prompted Hulagu Khan to pull the bulk of the Mongol forces out of the Middle East where they were poised to fight the Egyptian Mamluks (who defeated the remaining Mongols at Ain Jalut). 
Although Hulagu was allied with Kublai Khan, his forces were unable to help in the assault against the Song, due to Hulagu's war with the Golden Horde.Kublai continued the assault against the Song, gaining a temporary foothold on the southern banks of the Yangtze. Kublai made preparations to take Ezhou, but a pending civil war with his brother Ariq Böke—a rival claimant to the Mongol Khaganate—forced Kublai to move back north with the bulk of his forces. In Kublai's absence, the Song forces were ordered by Chancellor Jia Sidao to make an immediate assault and succeeded in pushing the Mongol forces back to the northern banks of the Yangtze. There were minor border skirmishes until 1265, when Kublai won a significant battle in Sichuan.From 1268 to 1273, Kublai blockaded the Yangtze River with his navy and besieged Xiangyang, the last obstacle in his way to invading the rich Yangtze River basin. Kublai officially declared the creation of the Yuan dynasty in 1271. In 1275, a Song force of 130,000 troops under Chancellor Jia Sidao was defeated by Kublai's newly appointed commander-in-chief, general Bayan. By 1276, most of the Song territory had been captured by Yuan forces, including the capital Lin'an.In the Battle of Yamen on the Pearl River Delta in 1279, the Yuan army, led by the general Zhang Hongfan, finally crushed the Song resistance. The last remaining ruler, the 8-year-old emperor Emperor Huaizong of Song, committed suicide, along with Prime Minister Lu Xiufu and 800 members of the royal clan. On Kublai's orders, carried out by his commander Bayan, the rest of the former imperial family of Song were unharmed; the deposed Emperor Gong was demoted, being given the title 'Duke of Ying', but was eventually exiled to Tibet where he took up a monastic life. The former emperor would eventually be forced to commit suicide under the orders of Kublai's great-great grandson, Gegeen Khan, out of fear that Emperor Gong would stage a coup to restore his reign. Other members of the Song Imperial Family continued to live in the Yuan dynasty, including Zhao Mengfu and Zhao Yong.
Hulagu Khan