In recent months, China has been advancing a concept that it had not used much before, that of its “core interests.”

Thus, President Hu Jintao, after talks with President Barack Obama, told the press that he had emphasized to the American leader that “what is important is to respect and accommodate each other’s core interests and major concerns.”

Just what does the term mean to China? A People’s Daily online article published after Obama left China explained that “core interests” is “a new code phrase meaning China’s claim of sovereignty over Taiwan, Xinjiang and Tibet.”

The “core interests” ploy is being used not just with the United States. A China-Australia joint statement issued last month also employed the term and Australia said that it “respects China’s sovereignty and territorial integrity, including in relation to Tibet and Xinjiang.” Taiwan was not included.

And did the Obama trip advance China’s core interests? The Chinese certainly think so. A joint statement issued by the two leaders said in part: “The two sides agreed that respecting each other’s core interests is extremely important to ensure steady progress in U.S.-China relations.”

China likes to nail the United States down to specific positions and, in particular, wants the American president to make such declarations on Chinese soil. Thus, in June 1998, while in Shanghai, then President Bill Clinton acceded to Beijing’s wishes and declared a “three no’s” policy regarding Taiwan.

The United States, said the president, does not support independence for Taiwan, or “two Chinas” or “one Taiwan one China,” and believed that Taiwan should not be a member of any international organization for which statehood is a requirement. Clinton was criticized for the remarks after returning to the United States.

This time, Beijing wanted the current American president to say publicly that Tibet is part of China. And Mr. Obama obliged.

Appearing before the media after talks with his Chinese counterpart, President Obama said: "We did note that while we recognize that Tibet is part of the People’s Republic of China, the United States supports the early resumption of dialogue between the Chinese government and representatives of the Dalai Lama to resolve any concerns and differences that the two sides may have."

That was what China wanted him to say. The bit about resuming a dialogue wasn’t important to Beijing since China has made it clear that such talks will not be about autonomy for Tibet but simply be on the personal status of the exiled Tibetan leader.

Beijing may well see progress on Taiwan as well. While President Ma Ying-jeou has said that he will only discuss economic issues with the mainland, at least in his first term, the U.S. appears to endorse a cross-strait political dialogue as well. In the joint statement, the United States "looks forward to efforts by both sides to increase dialogues and interactions in economic, political and other fields."

No wonder the People’s Daily article joyously proclaimed: "For the first time ever, political dialogue across Taiwan Straits has been related in a formal document signed by both China and the U.S."

And President Hu, in his press statement, quoted President Obama as having said “on various occasions” that the U.S. "respects China’s sovereignty and territorial integrity when it comes to the Taiwan question and other matters."

Raymond Burghardt, chairman of the American Institute in Taiwan, flew to Taipei to reassure nervous officials there that the United States only accepted Beijing’s sovereignty over Tibet and Xinjiang but not Taiwan, an assertion that was immediately rejected by the Chinese foreign ministry spokesman, who said that the "principle of respecting China’s sovereignty and territorial integrity absolutely applies to Taiwan."

All this is like the game of go, where pieces are placed on a board to capture space for yourself and to corner your opponent.

And it is clear what China’s next step is. In his media statement, President Hu spent some time building his case. "The two sides reaffirmed the fundamental principle of respecting each other's sovereignty and territorial integrity," he said. "Neither side supports any attempts by any force to undermine this principle. We will continue to act in the spirit of equality, mutual respect, and noninterference in each other's internal affairs."

Since the United States accepts these principles, Beijing will no doubt ask Washington not to permit Tibetan and Xinjiang “separatists” to operate on American soil. This could include visits by the Dalai Lama.

The United States, no doubt, is looking at the board and thinking of its next moves.