Related papers: Non-orientable Nurikabe
The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space are studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence,…
We construct the Matrix theory descriptions of M-theory on the Mobius strip and the Klein bottle. In a limit, these provide the matrix string theories for the CHL string and an orbifold of type IIA string theory.
In arXiv:math/0605587, the first two authors have constructed a gauge-equivariant Morse stratification on the space of connections on a principal U(n)-bundle over a connected, closed, nonorientable surface. This space can be identified with…
In this paper we present an explicit construction for the fundamental solution to the Dirac and Laplace operator on some non-orientable conformally flat manifolds. We first treat a class of projective cylinders and tori where we can study…
A longstanding avenue of research in orientable surface topology is to create and enumerate collections of curves in surfaces with certain intersection properties. We look for similar collections of curves in non-orientable surfaces. A…
We study curvatures of the groups of measure-preserving diffeomorphisms of non-orientable compact surfaces. For the cases of the Klein bottle and the real projective plane we compute curvatures, their asymptotics and the normalized Ricci…
This is the second of two companion papers dedicated to the investigation of vortex motion on non-orientable surfaces. The first paper of the pair is predominantly concerned with establishing the Hamiltonian approach to systems of point…
We investigate the motion of point vortices on the Mobius band and Klein bottle. Since these are non-orientable surfaces, the standard Hamiltonian approach does not apply. We therefore begin by establishing a modified Hamiltonian approach…
We study the relations between pin structures on a non-orientable even-dimensional manifold, with or without boundary, and pin structures on its orientable double cover, requiring the latter to be invariant under sheet-exchange. We show…
The problem of enumerating dimers on an M x N net embedded on non-orientable surfaces is considered. We solve both the Moebius strip and Klein bottle problems for all M and N with the aid of imaginary dimer weights. The use of imaginary…
We study explicit solutions for orientifolds of Matrix theory compactified on noncommutative torus. As quotients of torus, cylinder, Klein bottle and M\"obius strip are applicable as orientifolds. We calculate the solutions using Connes,…
We construct several examples of compactification of Type IIB theory on orientifolds and discuss their duals. In six dimensions we obtain models with $N=1$ supersymmetry, multiple tensor multiplets, and different gauge groups. In nine…
Which surfaces can be realized with two-dimensional faces of the five-dimensional cube (the penteract)? How can we visualize them? In recent work, Aveni, Govc, and Roldan, show that there exist 2690 connected closed cubical surfaces up to…
We investigate closed knight's tours on M\"obius strip and Klein bottle chess boards. In particular, we characterize the board dimensions that admit tours that are nullhomotopic and the board dimensions that admit tours that realize…
In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology that classifies their global shape.…
We extend to non-orientable surfaces previous work on sewing constraints in Conformal Field Theory. A new constraint, related to the real projective plane, is described and is used to illustrate the correspondence with a previous…
We consider non-perturbative six and four dimensional N=1 space-time supersymmetric orientifolds. Some states in such compactifications arise in ``twisted'' open string sectors which lack world-sheet description in terms of D-branes. Using…
In this thesis we deal with two different classes of variational problems: 1) the problem of closed curves with prescribed curvature, or $H$-loop problem; 2) the study of the nodal solutions of the fractional Brezis-Nirenberg problem. In…
We consider non-perturbative six dimensional N=1 space-time supersymmetric orientifolds of Type IIB on K3 with non-trivial NS-NS B-flux. All of these models are non-perturbative in both orientifold and heterotic pictures. Thus, some states…
This paper aims to define and study a notion of orientability in the Heisenberg sense ($\mathbb{H}$-orientability) for the Heisenberg group $\mathbb{H}^n$. In particular, we define such notion for $\mathbb{H}$-regular $1$-codimensional…