Related papers: Quaternionic complex manifolds and fixed-point set…

This paper deals with the question of J.Morava on existence of canonical complex cobordism class of singular submanifold. We present several solutions of this question for $X_r(\xi)$ -- the set of points where $\dim\xi-r+1$ generic sections…

Let the circle act effectively in a Hamiltonian fashion on a compact symplectic manifold $(M, \omega)$. Assume that the fixed point set $M^{S^1}$ has exactly two components, $X$ and $Y$, and that $\dim(X) + \dim(Y) +2 = \dim(M)$. We first…

Quadric complexes are square complexes satisfying a certain combinatorial nonpositive curvature condition. These complexes generalize 2-dimensional CAT(0) cube complexes and are a square analog of systolic complexes. We introduce and study…

We describe the $S^1$-action on the Quot-scheme $\Quot({\cal E}^n)$ associated to the trivial bundle ${\cal E}^n=CP^1\times{\smallBbb C}^n$. In particlular, the topology of the $S^1$-fixed-point components in $\Quot({\cal E}^n)$ and the…

For a circle action on a compact almost complex manifold with a fixed point, the lower bound on the number of fixed points is known in dimension up to 12 except 10. In this paper, we show that if the circle group acts on a 10-dimensional…

A general relation is derived for the action difference between two fixed points and a phase space area bounded by the irreducible component of a heteroclinic tangle. The determination of this area can require accurate calculation of…

Penrose's two-spinor notation for $4$-dimensional Lorentzian manifolds can be extended to two-component notation for quaternionic manifolds, which is a very useful tool for calculation. We construct a family of quaternionic complexes over…

We classify symplectic non-Hamiltonian circle actions on compact connected symplectic 4-manifolds, up to equivariant symplectomorphisms. Namely, we define a set of invariants, show that the set is complete, and determine which values are…

In this note we clarify the relevance of ``connections up to homotopy'' to the theory of characteristic classes. We have already remarked \cite{Crai} that such connections up to homotopy can be used to compute the classical Chern…

We consider 3-manifolds admitting the action of an involution such that its space of orbits is homeomorphic to $S^3.$ Such involutions are called \textit{hyperelliptic} as the manifolds admitting such an action. We prove that the sectional…

We will prove the following theorems. The first theorem posits the existence of a fixed point for the actions of nilpotent Lie groups on nonpositively curved compact manifolds. The second theorem states that actions of solvable Lie groups…

Maps between manifolds $M^m\to N^{m+\ell}$ ($\ell>0$) have multiple points, and more generally, multisingularities. The closure of the set of points where the map has a particular multisingularity is called the multisingularity locus. There…

Let $X$ be a Fano threefold and $\C ^* \times X\rightarrow X$ an algebraic action. Then $X$ has a $S^1$-invariant K\"ahler structure and the corresponding $S^1$-action admits an equivariant moment map which is at the same time a perfect…

Here we follow the basic analysis that is common for real and complex variables and find how it can be applied to a quaternionic variable. Non-commutativity of the quaternion algebra poses obstacles for the usual manipulations; but we show…

We present an approach to the spectrum and analytic functional calculus for quaternionic linear operators, following the corresponding results concerning the real linear operators. In fact, the construction of the analytic functional…

We use a quaternionic structure on the product of two symplectic manifolds for relating Liouvillian forms with linear symplectic maps obtained by the symplectic Cayley's transformation.

We construct closed symplectic manifolds for which spherical classes generate arbitrarily large subspaces in 2-homology, such that the first Chern class and cohomology class of the symplectic form both vanish on all spherical classes. We…

Due to the non-commutative nature of quaternions we introduce the concept of left and right action for quaternionic numbers. This gives the opportunity to manipulate appropriately the $H$-field. The standard problems arising in the…

Projective structures on compact real manifolds are classical objects in real differential geometry. Complex manifolds with a holomorphic projective structure on the other hand form a special class as soon as the dimension is greater than…

We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)\times O(N_2) \times O(N_3)$ transformations, of which the scalar fields form a…