Related papers: Isotropy in Group Cohomology

We consider an entropy-type invariant which measures the polynomial volume growth of submanifolds under the iterates of a map, and we establish sharp uniform lower bounds of this invariant for the following classes of symplectomorphisms of…

An automorphism $\alpha$ of a group $G$ is normal if it fixes every normal subgroup of $G$ setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively…

In any contact manifold of dimension $2n-1\geq 11$, we construct examples of closed legendrian submanifolds which are not diffeomorphic but whose lagrangian cylinders in the symplectization are hamiltonian isotopic.

A manifold is said to be $n$-plectic if it is equipped with a closed, nondegenerate $(n+1)$-form. This thesis develops the theory of \emph{relative $n$-plectic structures}, where the classical condition is replaced by a closed,…

Orthogonal or symplectic Yangians are defined by the Yang-Baxter $RLL$ relation involving the fundamental $R$ matrix with $so(n)$ or $sp(2m)$ symmetry. Simple $L$ operators with linear or quadratic dependence on the spectral parameter exist…

Dijkgraaf-Witten theories have a wide range of applications in topological phases of matter and the study of generalized global symmetries. We develop a method to construct BF-type Lagrangians for Dijkgraaf-Witten theories with non-abelian…

There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for any two functions f and g. We notice that this non-commutative differential algebra has a geometrical…

Given a Lagrangian submanifold $L$ in a symplectic manifold $X$, the homological Lagrangian monodromy group $\mathcal{H}_L$ describes how Hamiltonian diffeomorphisms of $X$ preserving $L$ setwise act on $H_*(L)$. We begin a systematic study…

We explore finitely generated groups by studying the nilpotent towers and the various Lie algebras attached to such groups. Our main goal is to relate an isomorphism extension problem in the Postnikov tower to the existence of certain…

A symplectic Lie group is a Lie group with a left-invariant symplectic form. Its Lie algebra structure is that of a quasi-Frobenius Lie algebra. In this note, we identify the groupoid analogue of a symplectic Lie group. We call the…

A rational group of hermitian type is an algebraic group over the rational numbers whose symmetric space is a hermitian symmetric space. We assume such a group $G$ to be given, which we assume is isotropic. Then, for any rational parabolic…

If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make…

In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…

This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…

Let $\mathfrak{Nil}$ be the class of nilpotent groups and $G$ be a group. We call $G$ a meta-$\mathfrak{Nil}$-Hamiltonian group if any of its non-$\mathfrak{Nil}$ subgroups is normal. Also, we call $G$ a para-$\mathfrak{Nil}$-Hamiltonian…

We analyze all possible symmetry reductions of Lagrangians that yield fully equivalent field equations for any 4-dimensional metric theory of gravity. Specifically, we present a complete list of infinitesimal group actions obeying the…

The Hopf-Galois structures on normal extensions $K/k$ with $G=Gal(K/k)$ are in one-to-one correspondence with the set of regular subgroups $N\leq B=Perm(G)$ that are normalized by the left regular representation $\lambda(G)\leq B$. Each…

The aim of this paper is to prove the following result. For any commutative formal group ${\frak F}(x\otimes 1,1\otimes x),$ which is considered as a formal group over $H_\mathbb{Q},$ there exists a homomorphism to a formal group of 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…

We study Lagrangian cobordism groups of closed symplectic surfaces of genus $g \geq 2$ whose relations are given by unobstructed, immersed Lagrangian cobordisms. Building upon work of Abouzaid and Perrier, we compute these cobordism groups…