# Circle actions on unitary manifolds

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Zhi Lü, Fudan University

Online Talk

In this talk, we pay much more attention on Kosniowski conjecture, saying that for a nonbounding unitary $S^1$-manifold fixing only isolated points,  the number of fixed points is greater than $\dim M/4$; in other words, $4\chi (M)>\dim M$, where $\chi(M)$ denotes the Euler characteristic of $M$. I will talk about a proof of this conjecture. Our argument can automatically be applied to the case of oriented $S^1$-manifolds, so we also can conclude that for a nonbounding oriented $S^1$-manifold fixing only isolated points,  $2\chi (M)>\dim M$.