Related papers: Formal loops, Tate objects and tangent Lie algebra…

Shifted symplectic Lie and $L_\infty$ algebroids model formal neighbourhoods of manifolds in shifted symplectic stacks, and serve as target spaces for twisted variants of classical AKSZ topological field theory. In this paper, we classify…

We consider canonical symplectic structure on the moduli space of flat ${\g}$-connections on a Riemann surface of genus $g$ with $n$ marked points. For ${\g}$ being a semisimple Lie algebra we obtain an explicit efficient formula for this…

We calculate the category of D-modules on the loop space of the affine line in coherent terms. Specifically, we find that this category is derived equivalent to the category of ind-coherent sheaves on the moduli space of rank one de Rham…

We exhibit a natural Lie algebra structure on the graded space of cyclic coinvariants of a symplectic vector space.

To any $\mathfrak{g}$-manifold $M$ are associated two dglas $\operatorname{tot}\big(\Lambda^{\bullet} \mathfrak{g}^\vee \otimes_{\Bbbk} T_{\operatorname{poly}}^{\bullet} \big)$ and $\operatorname{tot} \big(\Lambda^{\bullet}…

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt…

We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space…

We identify a new class of closed smooth manifolds for which there exists a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in a unit cotangent disk bundle, settling a well-known conjecture of…

Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. This setting…

Let $S$ be a Noetherian scheme, and let $X$ be a scheme over $S$, such that all relative symmetric powers of $X$ over $S$ exist. Assume that either $S$ is of pure characteristic $0$ or $X$ is flat over $S$. Assume also that the structural…

Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong…

In this paper, we provide a geometric characterization of virtual nonlinear nonholonomic constraints from a symplectic perspective. Under a transversality assumption, there is a unique control law making the trajectories of the associated…

We will develop a formal non-commutative (NC) deformation theory of smooth algebraic varieties $X$ defined over a field $k$, and describe a semi-universal deformation where the tangent space $T^1$ and the obstruction space $T^2$ are given…

This paper is the third in a series that researches the Morse Theory, gradient flows, concavity and complexity on smooth compact manifolds with boundary. Employing the local analytic models from \cite{K2}, for \emph{traversally generic…

We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various…

Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $\pi$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a…

We equip the whole tangent space $TM$ to a hyperbolic manifold $M$ (of constant sectional curvature -1) with a natural metric in an intrinsic way, so that the isometries of $M$ extend to isometries of $TM$ by holomorphic continuation. The…

This is a research monograph on symplectic cohomology (disguised as an advanced graduate textbook), which provides a construction of this version of Hamiltonian Floer cohomology for cotangent bundles of closed manifolds. The focus is on the…

We show that the quotient associated to a quasi-Hamiltonian space has a symplectic structure even when 1 is not a regular value of the momentum map: it is a disjoint union of symplectic manifolds of possibly different dimensions, which…

This paper is devoted to the study of the relation between `formal exponential maps,' the Atiyah class, and Kapranov $L_\infty[1]$ algebras associated with dg manifolds in the $C^\infty$ context. Given a dg manifold, we prove that a `formal…