Related papers: On Nearly Frobenius Structures

We investigate 7 dimensional almost para-contact metric structures induced by the 3-forms of $G_2^*$ Structures. We calculate the projections that determine to which class the almost para-contact structure belongs, by using the properties…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

We introduce the notion of almost unital and finite-dimensional (AUF) algebras, which are associative $\mathbb C$-algebras that may be non-unital or infinite-dimensional, but have sufficiently many idempotents. We show that the pseudotrace…

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. We classify these structures by their intrinsic torsion and review the literature in terms of this scheme. Moreover, we determine necessary and…

We prove a series of Approximation Theorems in the setting of Waldhausen quasicategories. These theorems, inspired by Waldhausen's 1985 Approximation Theorem, give sufficient conditions for an exact functor of Waldhausen quasicategories to…

An almost abelian Lie group is a solvable Lie group with a codimension-one normal abelian subgroup. We characterize almost Hermitian structures on almost abelian Lie groups where the almost complex structure is harmonic with respect to the…

We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine…

We describe the classification of ranked definably quasi-Frobenius groups of odd type : dihedral configurations are isomorphic to PGL(2, K) for K an algebraically closed field of characteristic other than two; Frobenius groups are spilt and…

In this paper we show that the convolution product of "almost characters" of a connected reductive group over a finite field is given by "structure constants" whose leading coefficients can be interpreted in K-theoretic terms and in…

I describe a project to open a new territory of quantum field theory where the fields live not on a space-time manifold but on certain complete metric spaces of (n-1)-dimensional objects (defects) in a 2n-dimensional space-time M. These…

These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…

Foams are surfaces with branch lines at which three sheets merge. They have been used in the categorification of sl(3) quantum knot invariants and also in physics. The 2D-TQFT of surfaces, on the other hand, is classified by means of…

Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in…

A construction that assigns a Boolean 1D TQFT with defects to a finite state automaton was recently developed by Gustafson, Im, Kaldawy, Khovanov, and Lihn. We show that the construction is functorial with respect to the category of finite…

For a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a…

In this paper we give a characterization of 2-dimensional topological field theories over a space $X$ as Frobenius bundles with connections over $LX$, the free loop space of $X$. This is a generalization of the folk theorem stating that…

The differential geometry of almost Grassmann structures defined on a differentiable manifold of dimension n = pq by a fibration of Segre cones SC (p, q) is studied. The peculiarities in the structure of almost Grassmann structures for the…

We extend a recent result of Pantev-Toen-Vaquie-Vezzosi, who constructed shifted symplectic structures on derived mapping stacks having a Calabi-Yau source and a shifted symplectic target. Their construction gives a clear conceptual…

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation…

This paper develops a novel approach to functorial quantum field theories (FQFTs) in the context of Lorentzian geometry. The key challenge is that globally hyperbolic Lorentzian bordisms between two Cauchy surfaces cannot change the…