Related papers: Circle actions on six dimensional oriented manifol…

Inspired by constructions of Kova\v{c}evi\'{c}, we introduce the amalgamated free product of circle actions, obtained by blowing up two actions along prescribed orbits and rearranging the inserted intervals. Under natural orbit and index…

Let $M$ be a symplectic manifold, equipped with a semifree symplectic circle action with a finite, nonempty fixed point set. We show that the circle action must be Hamiltonian, and $M$ must have the equivariant cohomology and Chern classes…

Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the…

Consider a Hamiltonian circle action on a closed $8$-dimensional symplectic manifold $M$ with exactly five fixed points, which is the smallest possible fixed set. In their paper, L. Godinho and S. Sabatini show that if $M$ satisfies an…

Let $(M,\omega_M)$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^1$-action. We show that if the minimal (or maximal) fixed component of the action is an isolated point, then…

Denote by $\mathcal{Z}_5((\mathbb{Z}_2)^3)$ the group, which is also a vector space over $\mathbb{Z}_2$, generated by equivariant unoriented bordism classes of all five-dimensional closed smooth manifolds with effective smooth…

Given an $S^1$-manifold with isolated fixed points, some recent papers are concerned with the relationship between the least number of fixed points and the characteristic numbers of this manifold, and their proofs have some similar…

Let $(X,\sigma,J)$ be a compact K\"{a}hler Calabi-Yau manifold equipped with a symplectic circle action. By Frankel's theorem \cite{F}, the action on $X$ is non-Hamiltonian and $X$ does not have any fixed point. In this paper, we will show…

We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry.

In this paper, we prove that if a finite group acts smoothly and effectively on an integral homology six-sphere and the fixed point set has an odd Euler characteristic, then the acting group is isomorphic to either the alternating group on…

The fixed-point spectrum of a locally compact second countable group G on lp is defined to be the set of real numbers p such that every action by affine isometries of G on lp admits a fixed-point. We show that this set is either empty, or…

We show that every real analytic action of a connected supersoluble Lie group on a compact surface with nonzero Euler characteristic has a fixed point. This implies that E. Lima's fixed point free $C^{\infty}$ action on $S^2$ of the affine…

We give bordism-finiteness results for manifolds with semi-simple group action. Consider the class of oriented manifolds which admit a circle action with isolated fixed points such that the action extends to an $S^3$-action with fixed…

We show that recent results of Friedl-Vidussi and Chen imply that a symplectic manifold admits a fixed point free circle action if and only if it admits a symplectic circle action and we give a complete description of the symplectic cone in…

We construct metrics of positive scalar curvature on manifolds with circle actions. One of our main results is that there exist $S^1$-invariant metrics of positive scalar curvature on every $S^1$-manifold which has a fixed point component…

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

The main result of this paper is a formula for calculating the Seiberg-Witten invariants of 4-manifolds with fixed-point free circle actions. This is done by showing under suitable conditions the existence of a diffeomorphism between the…

We study isometric actions of Steinberg groups on Hadamard manifolds. We prove some rigidity properties related to these actions. In Particular we show that every isometric action of $St_n(F_p\langle t_1,\ldots ,t_k \rangle)$ on Hadamard…

Let $M$ be a $2n$-dimensional closed symplectic manifold admitting a Hamiltonian circle action with isolated fixed points. We show that if $M$ contains an $S^1$-invariant symplectic hypersurface $D$ such that $M\setminus D$ is a homology…

We obtain a general lower bound for the number of fixed points of a circle action on a compact almost complex manifold $M$ of dimension $2n$ with nonempty fixed point set, provided the Chern number $c_1c_{n-1}[M]$ vanishes. The proof…