On circle actions with exactly three fixed points

Abstract

We study smooth, closed orientable $S^1$-manifolds $M$ with exactly $3$ fixed points. We show that the dimension of $M$ is of the form $4\cdot 2^a$ or $8\cdot (2^a+2^b)$ with $a,b\ge 0$ and $a\ne b$. Moreover, under the extra assumption that $M$ is spin or unitary we determine exactly the dimension of $M$.

10 pages, minor changes

References in corpus (5)

• Circle actions on almost complex manifolds with isolated fixed points
• Hamiltonian circle actions on eight dimensional manifolds with minimal fixed sets
• On dimensions supporting a rational projective plane
• Circle actions on almost complex manifolds with 4 fixed points
• Circle actions on 8-dimensional almost complex manifolds with 4 fixed points