Related papers: Revisiting pinors, spinors and orientability

In the spirit of Sullivan's paper "Cycles for the Dynamical Study of Foliated Manifolds and Complex Manifolds", existence of a contact structure on a closed manifold $M$ is shown to be equivalent to existence of an ample $S^1$-invariant…

We show that two $\operatorname{Pin}$-structures on a surface differ by a diffeomorphism of the surface if and only if they are cobordant (for comparison, the analogous fact has already been shown for $\operatorname{Spin}$-structures). We…

M(atrix) theory description is investigated for M-theory compactified on non-orientable manifolds. Relevant M(atrix) theory is obtained by Fourier transformation in a way consistent with T-duality. For nine-dimensional compactification on…

A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.

We consider surfaces with a double elliptic fibration, with two sections. We study the orbits under the induced translation automorphisms proving that, under natural conditions, the finite orbits are confined to a curve. This goes in a…

We study the Disc-structure space $S^{\rm Disc}_\partial(M)$ of a compact smooth manifold $M$. Informally speaking, this space measures the difference between $M$, together with its diffeomorphisms, and the diagram of ordered framed…

Let M be a closed oriented 4-manifold, with Riemannian metric g, and a spin^C structure induced by an almost-complex structure \omega. Each connection A on the determinant line bundle induces a unique connection \nabla^A, and Dirac operator…

Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common…

We introduce a diffeomorphism invariant of $4$-manifolds, the $\mathrm{Pin}^-(2)$-monopole invariant, defined by using the $\mathrm{Pin}^-(2)$-monopole equations. We compute the invariants of several $4$-manifolds, and prove gluing…

We show that the numbers of generations and anti-generations of a (2,2) string compactification with diagonal internal theory can be expressed in terms of certain specifications of the elliptic genus of the untwisted internal theory which…

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact…

We define Hitchin's moduli space for a principal bundle $P$, whose structure group is a compact semisimple Lie group $K$, over a compact non-orientable Riemannian manifold $M$. We use the Donaldson-Corlette correspondence, which identifies…

The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by…

In this note, we examine how the BKP structure of the generating series of several models of maps on non-oriented surfaces can be used to obtain explicit and/or efficient recurrence formulas for their enumeration according to the genus and…

We prove rigidity results describing contextually-constrained maps defined on Grassmannians and manifolds of ordered independent line tuples in finite-dimensional vector or Hilbert spaces. One statement in the spirit of the Fundamental…

We study the non-linear Dirichlet-to-Neumann map for the Poincar\'e-Einstein filling problem. For even dimensional manifolds the range of this non-local map is described in terms of a rank two "Dirichlet-to Neumann tensor" along the…

Fine questions our interpretation of unidirectional-stripes over bidirectional-checkerboard, and illustrates his criticism by simulating a momentum space structure consistent with our data and corresponding to a checkerboard-looking real…

Let $M$ be an oriented closed 4-manifold and $\cL$ be a $spin^c$ structure on $M$. In this paper we prove that under a suitable condition the Seiberg-Witten moduli space has a canonical spin structure and its spin bordism class is an…

Generalised spin structures are necessary for placing fermions on manifolds that do not admit a standard spin structure. This is especially relevant in a dimensional reduction on such a manifold, which can then be compensated by using…

In this manuscript, we formulate a (1+1)-dimensional Jackiw-Teitelboim gravity toy model whose Euclidean spacetime manifold is the M\"obius band $M$. Since $M$ is non-orientable, the relevant spin-statistics structure is Pin rather than…