Related papers: New tools for classifying Hamiltonian circle actio…

Let $\Gamma$ be a discrete group with property $(T)$ of Kazhdan. We prove that any Riemannian isometric action of $\Gamma$ on a compact manifold $X$ is locally rigid. We also prove a more general foliated version of this result. The…

Let M be a closed simply connected n-manifold of positive sectional curvature. We determine its homeomorphism or homotopic type if M also admits an isometric elementary p-group action of large rank. Our main results are: There exists a…

For manifolds equipped with group actions, we have the following natural question: To what extent does the equivariant cohomology determine the equivariant diffeotype? We resolve this question for Hamiltonian circle actions on compact,…

This is a slightly altered version of the authors thesis from 2014. In the first main part we show that the quotient space of a compact, simply connected and nonnegatively curved Riemannian 4-manifold by an effective, isometric…

In this paper, we compute the homotopy type of the group of equivariant symplectomorphisms of $S^2 \times S^2$ and $\mathbb{C}P^2 \# \overline{\mathbb{C}P^2}$ under the presence of Hamiltonian group actions of the circle $S^1$. We prove…

We prove that when Hodge theory survives on non-compact symplectic manifolds, a compact symplectic Lie group action having fixed points is necessarily Hamiltonian, provided the associated almost complex structure preserves the space of…

A study of symplectic actions of a finite group $G$ on smooth 4-manifolds is initiated. The central new idea is the use of $G$-equivariant Seiberg-Witten-Taubes theory in studying the structure of the fixed-point set of these symmetries.…

We determine conditions under which two Hamiltonian torus actions on a symplectic manifold $M$ are homotopic by a family of Hamiltonian torus actions, when $M$ is a toric manifold and when $M$ is a coadjoint orbit.

Let X be a compact manifold with a smooth action of a compact connected Lie group G. Let $L\to X$ be a complex line bundle. Using the Cartan complex for equivariant cohomology, we give a new proof of a theorem of Hattori and Yoshida which…

We study the problem of determining which diffeomorphism classes of K\"{a}hler manifolds admit a Hamiltonian circle action. Our main result is the following: Let $M$ be a closed symplectic manifold, diffeomorphic to a complete intersection…

Let \((M,\omega)\) be a compact symplectic manifold of dimension \(2n\) endowed with a Hamiltonian circle action with only isolated fixed points. Whenever \(M\) admits a toric \(1\)-skeleton \(\mathcal{S}\), which is a special collection of…

We construct a non-Hamiltonian symplectic circle action on a closed, connected, six-dimensional symplectic manifold with exactly 32 fixed points.

It is known that an isometric action of a Lie group on a compact symmetric space gives rise to a proper Fredholm action of a path group on a path space via the gauge transformations. In this paper, supposing that the isometric action is a…

For any compact connected Lie group $G$, we study the Hamiltonian sum of two compact Hamiltonian group $G$-manifolds $(X^+,\omega^+,\mu^+)$ and $(X^-,\omega^-,\mu^-)$ with a common codimension 2 Hamiltonian submanifold $Z$ of the opposite…

We consider symplectic manifolds with Hamiltonian torus actions which are "almost but not quite completely integrable": the dimension of the torus is one less than half the dimension of the manifold. We provide a complete set of invariants…

We study the core of a proper action by a Lie group $G$ on a smooth manifold $M$, extending the construction for $G$ compact by Skjelbred and Straume. Moreover, we show that many properties of a proper $G$-action on $M$ are determined by…

In this note we prove that if a closed monotone symplectic manifold $M$ of dimension $2n,$ satisfying a homological condition that holds in particular when the minimal Chern number is $N>n,$ admits a Hamiltonian pseudo-rotation, then the…

In this paper, we classify the fixed point data (weights and signs at the fixed points), of a circle action on a 6-dimensional compact oriented manifold with 4 fixed points. We prove that it agrees with that of a disjoint union of rotations…

A Hamiltonian circle action on a compact symplectic manifold is known to be a closed geodesic with respect to the Hofer metric on the group of Hamiltonian diffeomorphisms. If the momentum map attains its minimum or maximum at an isolated…

This paper studies the question of when a loop $\phi$ in the group Symp$(M,\omega)$ of symplectomorphisms of a symplectic manifold $(M,\omega)$ is isotopic to a loop that is generated by a time-dependent Hamiltonian function. (Loops with…