Related papers: Semi-free actions with manifold orbit spaces

We show that a closed, simply-connected, non-negatively curved 5-manifold admitting an effective, isometric $T^2$ action is diffeomorphic to one of $S^5$, $S^3\times S^2$, $S^3\tilde{\times} S^2$ (the non-trivial $S^3$-bundle over $S^2$) or…

A finite nonabelian simple group does not admit a free action on a homology sphere, and the only finite simple group which acts on a homology sphere with at most 0-dimensional fixed point sets ("pseudofree action") is the alternating group…

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…

We study which lens spaces can bound smooth 4-manifolds with second Betti number one under various topological conditions. Specifically, we show that there are infinite families of lens spaces that bound compact, simply-connected, smooth…

A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and…

Let the compact torus $T^{n-1}$ act on a smooth compact manifold $X^{2n}$ effectively with nonempty finite set of fixed points. We pose the question: what can be said about the orbit space $X^{2n}/T^{n-1}$ if the action is cohomologically…

A (quasi-)Hamiltonian manifold is called multiplicity free if all of its symplectic reductions are 0-dimensional. In this paper, we classify multiplicity free Hamiltonian actions for (twisted) loop groups or, equivalently, multiplicity free…

In this note we derive an upper bound on the number of 2-spheres in the fixed point set of a smooth and homologically trivial cyclic group action of prime order on a simply-connected 4-manifold. This improves the a priori bound which is…

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…

We construct the first example of a 5-dimensional simply connected compact manifold that admits a K-contact structure but does not admit a semi-regular Sasakian structure. For this, we need two ingredients: (a) to construct a suitable…

The orbit-fixing deformation spaces of $C^\infty$ locally free actions of simply connected Lie groups on closed $C^\infty$ manifolds have been studied by several authors. In this paper we reformulate the deformation space by imitating the…

We show that every closed, simply connected, spin topological 4-manifold except $S^4$ and $S^2\times S^2$ admits a homologically trivial, pseudofree, locally linear action of $\mathbb{Z}_p$ for any sufficiently large prime number $p$ which…

Motivated by a problem of Hirzebruch, we study $8$-dimensional, closed, symplectic manifolds having a Hamiltonian torus action with isolated fixed points and second Betti number equal to $1$. Such manifolds are automatically positive…

An arrow matrix is a matrix with zeroes outside the main diagonal, first row, and first column. We consider the space $M_{St_n,\lambda}$ of Hermitian arrow $(n+1)\times (n+1)$-matrices with fixed simple spectrum $\lambda$. We prove that…

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…

Let $(M,\omega)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $\mu:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to…

In this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2 cohomology algebra of the orbit space of an arbitrary free $\mathbb{Z}_2$ and…

Given a smooth partial action $\alpha$ of a Lie groupoid $G$ on a smooth manifold $M,$ we provide necessary and sufficient conditions for $\alpha$ to be globalizable with smooth globalization. As an application, we provide results on the…

We study closed, simply connected manifolds with positive $2^\mathrm{nd}$-intermediate Ricci curvature and large symmetry rank. In odd dimensions, we show that they are spheres. In even dimensions other than $6$, we show that they must have…

In this work, it is shown that a simply-connected, rationally-elliptic torus orbifold is equivariantly rationally homotopy equivalent to the quotient of a product of spheres by an almost-free, linear torus action, where this torus has rank…