Related papers: Vector fields on mapping spaces and a converse to …
In this paper, we consider the following two algebraic hypersurfaces $$S^1\times S^2=\{(x_1,x_2,x_3,x_4)\in \mathbb{R}^4:(x_1^2+x_2^2-a^2)^2 + x_3^2 + x_4^2 -1=0;~ a>1\}$$ and $$S^2\times S^1=\{(x_1,x_2,x_3,x_4)\in…
There is an important difference between Hamiltonian-like vector fields in an almost-symplectic manifold $(M,\sigma)$, compared to the standard case of a symplectic manifold: in the almost-symplectic case, a vector field such that the…
We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…
The general linear group acts on the space of several linear maps on the vector space as the basis change. Similarly, we have the actions of the orthogonal and symplectic groups. Generators and identities for the corresponding polynomial…
We construct the Feigin-Stoyanovsky (combinatorial) basis in case of one-dimensional lattice vertex superalgebras $V_{\sqrt{N}\,\mathbb{Z}}$. Our proof is based on invariance of semi-infinite monomials linear span under action of…
We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of…
We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of the A- and B-models which involves a doubling of coordinates, and can be understood as a complexification of the Poisson $\sigma$-model…
In this paper we will prove a super-analogue of a well-known result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology…
We analyse the algebras generated by free component quantum fields together with the susy generators $Q,\bar Q$. Restricting to hermitian fields we first construct the scalar field algebra from which various scalar superfields can be…
We use the Bar-Natan Zh-correspondence to identify the generalized Alexander polynomial of a virtual knot with the Alexander polynomial of a two component welded link. We show that the Zh-map is functorial under concordance, and also that…
We introduce natural differential geometric structures underlying the Poisson-Vlasov equations in momentum variables. We decompose the space of all vector fields over particle phase space into a semi-direct product algebra of Hamiltonian…
We discuss a natural extension of the AKSZ construction to the case where the source is given by a supermanifold with a chosen integral form. We then focus on the special case with the target given by a Courant algebroid. In the simplest…
In the time evolution of fluids, the topologies of fluids can be changed by the creations and annihilations of singular points and by switching combinatorial structures of separatrices. In this paper, to describe the possible generic time…
We prove the AKSZ theorem for shifted Poisson structures: if $X$ is an $n$-shifted Poisson derived stack, and $Y$ a $d$-oriented derived stack, then the mapping stack \[\underline{\mathrm{Map}}(Y,X)\] is naturally endowed with an…
This article investigates the complex symplectic geometry of the deformation space of complex projective structures on a closed oriented surface of genus at least 2. The cotangent symplectic structure given by the Schwarzian parametrization…
In this note we present some abstract ideas how one can construct spaces from building blocks according to a graph. The coupling is expressed via boundary pairs, and can be applied to very different spaces such as discrete graphs, quantum…
We show that in multidimensional gravity vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists in all spatial dimensions and for all…
Kontsevich constructed a map between `good' graph cocycles $\gamma$ and infinitesimal deformations of Poisson bivectors on affine manifolds, that is, Poisson cocycles in the second Lichnerowicz--Poisson cohomology. For the tetrahedral graph…
We provide a unified construction of the symplectic forms which arise in the solution of both N=2 supersymmetric Yang-Mills theories and soliton equations. Their phase spaces are Jacobian-type bundles over the leaves of a foliation in a…
A proof of Sharkovsky's Theorem is given. It is shown how this proof naturally generalizes to looking at maps on graphs and to Sharkovsky-type theorems for these maps. The paper is written at an elementary level and is meant as an…