Speaker：Zhuangdan Guan（Henan University）

Time：2021-07-24 10:30

Location：Tencent Meeting ID：901 2531 9369（Password:202107）

Abstract:

This is a join work with Professor Wang Zhonghua. There is a long standing question: Is there a complex structure on the six dimensional sphere? Someone call this problem a complex Poincare problem, while someone call it the Chern’s last Theorem. After Chern claimed a proof for the nonexistence before he passed away, Professor Etesi gave a positive proof. It was published in 2015. However, none knew his proof was correct or not. In fact, Professor Atiyah gave a negative proof in 2016, for which none knew it is correct or not. In 2020, I published a paper in Pacific Journal of Mathematics, implying that Etesi’s further claim was completely wrong. Recently, we gave a further and clearer proof that Etesi’s further claim was wrong and we found a critical gap in Etesi’s published proof. The gap is related to the gauge group. We further found a way to check the gap with the complex five hyperquadratic as the projective tangent bundle of the six sphere. We then overcome the gap. So the question still remains.