Related papers: Frobenius Pairs and Atiyah Duality
Given an exact functor between triangulated categories which admits both adjoints and whose cotwist is either zero or an autoequivalence, we show how to associate a unique full triangulated subcategory of the codomain on which the functor…
In this note, we study submanifold geometry of the Atiyah-Hitchin manifold, the double cover of the $2$-monopole moduli space. When the manifold is naturally identified as the total space of a line bundle over $S^2$, the zero section is a…
We construct a duality for F-manifolds with eventual identities and special families of connections and we describe its interactions with several well-known constructions from the theory of Frobenius and F-manifolds.
The present paper investigates a natural generalization of the duality between Riemannian symmetric pairs of compact type and those of non-compact type \`a la \'E. Cartan. The main result of this paper is to construct an explicit…
Let $G$ be a group. We give a categorical definition of the $G$-equivariant $\alpha$-induction associated with a given $G$-equivariant Frobenius algebra in a $G$-braided multitensor category, which generalizes the $\alpha$-induction for…
This paper is a study of monoidal categories with duals where the tensor product need not be commutative. The motivating examples are categories of representations of Hopf algebras and the motivating application is the definition of…
This work continues the study of $F$--manifolds $(M,\circ)$, first defined by Hertling and Manin and investigated in [He]. The notion of a compatible flat structure $\nabla$ is introduced, and it is shown that many constructions known for…
The classical duality theory associates to an abelian group a dual companion. Passing to a non-abelian group, a dual object can still be defined, but it is no longer a group. The search for a broader category which should include both the…
We obtain polynomial Frobenius manifolds from classical $W$-algebras associated to regular nilpotent elements in simple Lie algebras using the related opposite Cartan subalgebras.
To characterize categorical constraints - associativity, commutativity and monoidality - in the context of quasimonoidal categories, from a cohomological point of view, we define the notion of a parity (quasi)complex. Applied to groups…
We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in…
Mason and Ng have given a generalization to semisimple quasi-Hopf algebras of Linchenko and Montgomery's generalization to semisimple Hopf algebras of the classical Frobenius-Schur theorem for group representations. We give a simplified…
Cohomology of a compatible family of Lie algebroids defined on a family of transverse manifolds is defined. A sheaf of differential forms on a compatible family of Lie algebroids defined over regular open subsets of a simplicial complex is…
Let $ G^\tau $ be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfeld structure of Poisson group; let $ H^\tau $ be its dual Poisson group. By means of Drinfeld's double construction and…
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…
A Riemannian metric is called Hessian if, locally, it can be written as the Hessian of a function called the Hessian potential. A (flat) Manin-Frobenius manifold is a flat Riemannian manifold furnished with a commutative and associative…
We construct several examples where duality transformation commutes with the orbifolding procedure even when the orbifolding group does not act freely, and there are massless states from the twisted sector at a generic point in the moduli…
In this paper we describe a homotopy torsion theory in the category of small symmetric monoidal categories. Thanks to the use of natural isomorphisms as basis for the nullhomotopy structure, this homotopy torsion theory enjoys some…
We show that, for a finite spectrum $X$, Spanier-Whitehead duality induces an isomorphism between the cohomological and homological Atiyah-Hirzebruch spectral sequences. As an application, it follows that Poincar\'e duality for a Poincar\'e…
Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian…