相关论文: Nilpotence in the symplectic bordism ring

In this note we show that the nilpotence conjecture for toric varieties is true over any regular coefficient ring containing Q.

We prove that there exists at least one close orbit in a given contact hypersurface in some symplectic manifolds.

A group is called capable if it is a central factor group. We consider the capability of certain nilpotent products of cyclic groups, and obtain a generalisation of a theorem of Baer for the small class case. The approach may also be used…

If X is a symplectic variety emedded in an affine space as a complete intersection of homogeneous polynomials, then X coincides with the nilpotent variety of a semisimple Lie algebra.

A group is called capable if it is a central factor group. We consider the capability of nilpotent products of cyclic groups, and obtain a generalization of a theorem of Baer for the metabelian small class case. The approach is also used to…

In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has infinitely many concave symplectic fillings and that all overtwisted contact 3-manifolds are…

We study the symplectic semi-characteristic of a closed 4n-dimensional symplectic manifold. First, using the even-degree part of the primitive cohomology, we define the symplectic semi-characteristic. Second, using a vector field with…

We study piecewise linear knot diagrams in the base of almost toric fibrations of symplectic four-manifolds. These diagrams translate to deformations of the almost toric fibration. We give several applications to symplectic topology, among…

We explain how a version of Floer homology can be used as an invariant of symplectic manifolds with $b_1>0$. As a concrete example, we look at four-manifolds produced from braids by a surgery construction. The outcome shows that the…

We provide a classification of congruence-simple semirings with a multiplicatively absorbing element and without non-trivial nilpotent elements.

In this paper we finish our classification of nilpotent symplectic alternating algebras of dimension 10 over any field F.

We establish an existence $h$-principle for symplectic cobordisms of dimension $2n>4$ with concave overtwisted contact boundary.

In line with known results on groups, we show the existence of the nilpotent radical in Lie rings with minimal condition on centralizers. We also prove a form of Engel's theorem if the characteristic is zero.

We prove a nilpotency theorem for the Bauer-Furuta stable homotopy Seiberg-Witten invariants for smooth closed 4-manifolds with trivial first Betti number.

In this paper, we systematically investigate the nilpotentizer and nilpotent graph for a Lie superalgebra over the field of characteristic not equal to 2. First, we establish some fundamental properties of the nilpotentizer. Next, we show…

The behavior of nilpotents can reveal valuable information about the algebra. We give a simple proof of a classic result that a finite ring is commutative if all its nilpotents lie in the center.

We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.

We formulate and prove that there are "abundant" in nilpotent orbits in real semisimple Lie algebras, in the following sense. If S denotes the collection of hyperbolic elements corresponding the weighted Dynkin diagrams coming from…

This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…

Necessary conditions for asymptotic stability and stabilizability of subsets for dynamical and control systems are obtained. The main necessary condition is homotopical and is in turn used to obtain a homological one. A certain extension is…