Related papers: Combinatorial spin structures on triangulated mani…
Exotic spinors arise in non-simply connected base manifolds due to the nonequivalent spinor structure. The dynamics of exotic spinors are endowed with an additional differential factor. In this work, we merge the exotic spinor scenario with…
We describe the different classes of $\mathrm{Spin(7)}$ structures in terms of spinorial equations. We relate them to the spinorial description of $\mathrm{G}_2$ structures in some geometrical situations. Our approach enables us to analyze…
We give a necessary and suffcient condition for almost-flat manifolds with cyclic holonomy to admit a Spin structure. Using this condition we find all 4-dimensional orientable almost- flat manifolds with cyclic holonomy that do not admit a…
Triangle presentations are combinatorial structures on finite projective geometries which characterize groups acting simply transitively on the vertices of a locally finite building of type $\tilde{\text{A}}_{n-1}$ ($n\ge3$). From a type…
Any oriented Riemannian manifold with a Spin-structure defines a spectral triple, so the spectral triple can be regarded as a noncommutative Spin-manifold. Otherwise for any unoriented Riemannian manifold there is the two-fold covering by…
The spaces of triangulations of a given manifold have been widely studied. The celebrated theorem of Pachner~\cite{Pachner} says that any two triangulations of a given manifold can be connected by a sequence of bistellar moves, or Pachner…
We develop a tighter implementation of basic PL topology, which keeps track of some combinatorial structure beyond PL homeomorphism type. With this technique we clarify some aspects of PL transversality and give combinatorial proofs of a…
The Matveev-Piergallini (MP) moves on spines of $3$-manifolds are well-known for their correspondence to the Pachner $2$-$3$ moves in dual ideal triangulations. Benedetti and Petronio introduced combinatorial descriptions of closed…
We prove that a planar graph is generically rigid in the plane if and only if it can be embedded as a pseudo-triangulation. This generalizes the main result of math.CO/0307347 which treats the minimally generically rigid case. The proof…
We define spin-c prequantization of a symplectic manifold to be a spin-c structure and a connection which are compatible with the symplectic form. We describe the cutting of an S^1-equivariant spin-c prequantization. The cutting process…
We present some basic results on a natural Poisson structure on any compact symmetric space. The symplectic leaves of this structure are related to the orbits of the corresponding real semisimple group on the complex flag manifold.
In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in…
We investigate topological properties of the moduli space of spin structures over genus two curves. In particular, we provide a combinatorial description of this space and give a presentation of the (rational) cohomology ring via generators…
This article gives a geometric interpretation of the spin base formulation with local spin base invariance of spinors on a curved space-time and in particular of a central element, the global Dirac structure, in terms of principal and…
We present a method of computing elements of spin groups in the case of arbitrary dimension. This method generalizes Hestenes method for the case of dimension 4. We use the method of averaging in Clifford's geometric algebra previously…
In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel…
$CPT$ groups of higher spin fields are defined in the framework of automorphism groups of Clifford algebras associated with the complex representations of the proper orthochronous Lorentz group. Higher spin fields are understood as the…
By some SL(2, Z) modular forms introduced in [4] and [9], we construct some {\Gamma}^0(2) and {\Gamma}_0(2) modular forms and obtain some new cancellation formulas for spin manifolds and spin^c manifolds respectively. As corollaries, we get…
We study spin structures on compact simply-connected homogeneous pseudo-Riemannian manifolds (M = G/H, g) of a compact semisimple Lie group G. We classify flag manifolds F = G/H of a compact simple Lie group which are spin. This yields also…
We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures…