Related papers: Regular F -manifolds with eventual identities
We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called "genus two G-function".…
Recently, it was shown that a rich class of second-order (maximally) superintegrable systems has an underpinning Hesse-Frobenius structure, i.e.\ a Frobenius structure that is compatible with a Hessian structure such that the Hessian…
We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the subbundle S defines the structure of a Levi-flat…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
Let S be a basic closed semi-algebraic set in R^n and P the corresponding preordering in R[X_1,...,X_n]. We examine for which polynomials f there exist identities f+\ep q \in P for all \ep>0. These are precisely the elements of the…
We consider the concept of a generalised manifold in the O(d,d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are…
We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the…
A Nijenhuis mock-Lie algebra is a mock-Lie algebra equipped with a Nijenhuis operator. The purpose of this paper is to extend the well-known results about Nijenhuis mock-Lie algebras to the realm of mock-Lie bialgebras. It aims to…
We generalise the concept of duality to systems of ordinary difference equations (or maps). We propose a procedure to construct a chain of systems of equations which are dual, with respect to an integral $H$, to the given system, by…
In this paper we show that a parallel differential form $\Psi$ of even degree on a Riemannian manifold allows to define a natural differential both on $\Omega^\ast(M)$ and $\Omega^\ast(M, TM)$, defined via the Fr\"olicher-Nijenhuis bracket.…
In the first part of this paper, we give a new analytical proof of a theorem of C. Sabbah on integrable deformations of meromorphic connections on $\mathbb P^1$ with coalescing irregular singularities of Poincar\'e rank 1, and generalizing…
Characterizing face-number-related invariants of a given class of simplicial complexes has been a central topic in combinatorial topology. In this regard, one of the well-known invariants is $g_2$. Let $K$ be a normal $3$-pseudomanifold…
We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field $\mathbb K$ of characteristic $\neq 2$ from scratch. We show that the formal model…
The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open…
We define a notion of "Frobenius pair", which is a mild generalization of the notion of Frobenius object in a monoidal category. We then show that Atiyah duality for smooth manifolds can be encapsulated in the statement that a certain…
Hexagon relations are algebraic realizations of four-dimensional Pachner moves, and there are hexagon relations admitting nontrivial cohomologies and leading thus to piecewise linear (PL) 4-manifold invariants. We show that some - but not…
On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…
We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.
We study an elliptic differential operator A on a manifold with conic points. Assuming A to be defined on the smooth functions supported away from the singularities, we first address the question of possible closed extensions of A to L^p…
In this paper, we give some new and interesting identities which are derived from the basis of Frobenius-Euler. Recently, Simsek et als(see [13]) have given some identities of q-analogue of Frobenius-Euler polynomials related to q-Bernstein…