Related papers: Graphs for torus actions on oriented manifolds wit…

This is the second of two papers but has been written so as to have minimal dependence on the first paper (which is also on this archive). Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete…

Let T be a torus of dimension at least k and M a T-manifold. M is a GKM_k-manifold if the action is equivariantly formal, has only isolated fixed points, and any k weights of the isotropy representation in the fixed points are linearly…

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…

For an endomorphism $s:V\rightarrow V$ of a finite dimensional complex vector space and an action of a torus $T$ on the full flag variety $\text{GL}_n({\mathbb C})/B$, we give a description of its fixed point set when $s$ is semisimple or…

We construct smooth $\mathbb{C}^*$-actions on the moduli spaces of super $J$-holomorphic curves as well as super stable curves and super stable maps of genus zero and fixed tree type such that their reduced spaces are torus invariant.…

Let $G$ be a connected compact Lie group, and let $M$ be a connected Hamiltonian $G$-manifold with equivariant moment map $\phi$. We prove that if there is a simply connected orbit $G\cdot x$, then $\pi_1(M)\cong\pi_1(M/G)$; if additionally…

It is well-known by the work of Hsiang and Kleiner that every closed oriented positively curved 4-dimensional manifold with an effective isometric S^1-action is homeomorphic to S^4 or CP^2. As stated, it is a topological classification. The…

Consider a holomorphic torus action on vector bundles over a complex manifold which lifts to a holomorphic vector bundle. When the connected components of the fixed-point set are partially ordered, we construct, using sheaf-theoretical…

We study finite group actions on smooth manifolds of the form $M\#\Sigma$, where $\Sigma$ is an exotic $n$-sphere and $M$ is a closed aspherical space form. We give a classification result for free actions of finite groups on $M\#\Sigma$…

We show that any effective isometric torus action of maximal rank on a compact Riemannian manifold with positive (sectional) curvature and maximal symmetry rank, that is, on a positively curved sphere, lens space, complex or real projective…

We show that the groupoids of two directed graphs are isomorphic if and only if the two graphs are orbit equivalent by an orbit equivalence that preserves isolated eventually periodic points. We also give a complete description of the…

In this paper we study a specific class of actions of a $2$-torus $\mathbb{Z}_2^k$ on manifolds, namely, the actions of complexity one in general position. We describe the orbit space of equivariantly formal $2$-torus actions of complexity…

In this present paper we study geometry of compact complex manifolds equipped with a \emph{maximal} torus $T=(S^1)^k$ action. We give two equivalent constructions providing examples of such manifolds given a simplicial fan $\Sigma$ and a…

We establish a necessary and sufficient condition for pairs of integers to arise as the weights at the fixed points of an effective circle action on a compact almost complex 4-manifold with a discrete fixed point set. As an application, we…

To a closed braid in a solid torus we associate a trace graph in a thickened torus in such a way that closed braids are isotopic if and only if their trace graphs can be related by trihedral and tetraherdal moves. For closed braids with a…

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…

The main result is a classification of smooth actions of $SL(n,{\bf R})$, $n \geq 3$, or connected groups locally isomorphic to it, on closed $n$-manifolds, extending a theorem of Uchida. We construct new exotic actions of $SL(n,{\bf Z})$…

We construct a model for the space of automorphisms of a connected p-compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer…

We present a simple approach to questions of topological orbit equivalence for actions of countable groups on topological and smooth manifolds. For example, for any action of a countable group $\Gamma$ on a topological manifold where the…

We develop a graphical calculus of manifold diagrams which generalises string and surface diagrams to arbitrary dimensions. Manifold diagrams are pasting diagrams for $(\infty, n)$-categories that admit a semi-strict composition operation…