Related papers: Spin cobordism categories in low dimensions
Subword complexes were defined by A.Knutson and E.Miller in 2004 for describing Gr\"obner degenerations of matrix Schubert varieties. The facets of such a complex are indexed by pipe dreams, or, equivalently, by the monomials in the…
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…
A new formula is obtained in algebraic topology, in terms of Betti numbers, and a new method, called the spinal method, is suggested and developed for generating quadrangulations of closed orientable surfaces. Those surfaces arise as the…
Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension are studied. Such structures are constructed on hyperspheres in 4-dimensional spaces, Euclidean and pseudo-Euclidean, respectively. The obtained manifolds…
We study chiral algebras in the $\bar{Q}$-cohomology of two dimensional SYK models with extended supersymmetry. In a special limit discovered in arXiv:1805.09325, we are able to construct explicitly a "vertical" single-particle higher-spin…
We relate the recently defined spectral torsion with the algebraic torsion of noncommutative differential calculi on the example of the almost-commutative geometry of the product of a closed oriented Riemannian spin manifold $M$ with the…
Spin states of two-dimensional Wigner clusters are considered at low temperatures, when all electrons are in ground coordinate states. The spin subsystem behavior is determined by antiferromagnetic exchange integrals. The spin states in…
We define and discuss an extension of the SpinC quantization concept to odd-dimensional manifolds. After that we describe its relation to (the usual) even-dimensional SpinC quantization and how its famous properties like "Quantization…
The paper is a colloquial-style discussion of invariants of algebraic surfaces analogous to the Donaldson polynomials, arising from moduli spaces of ``jumping'' Yang--Mills instantons, or moduli spaces of jumping vector bundles. The…
We consider a class of spin systems on randomly triangulated surfaces as discrete approximations to conformal matter fields coupled to 2d gravity. On the basis of certain universality assumptions we argue that at critical points with…
We analyze the low-energy spin structure of the nucleon in a covariant effective field theory with explicit spin-3/2 degrees of freedom to third order in the small scale expansion. Using the available data on the strong and electromagnetic…
This paper examines the category C^k_{d,n} whose morphisms are d-dimensional smooth manifolds that are properly embedded in the product of a k-dimensional cube with an (d+n-k)-dimensional Euclidean space. There are k directions to compose…
Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension. Near-minima of random functions also play an important role in high-dimensional statistics and…
The Seiberg-Witten equation with multiple spinors generalises the classical Seiberg-Witten equation in dimension three. In contrast to the classical case, the moduli space of solutions $\mathcal{M}$ can be non-compact due to the appearance…
In this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space $M_\Sigma$ with singular stratum $\beta M$ (a closed manifold of positive codimension) and associated link equal to…
We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin$^{c, r}$ structure carrying a…
We describe off-shell $\mathcal{N}=1$ M-theory compactifications down to four dimensions in terms of eight-dimensional manifolds equipped with a topological $Spin(7)$-structure. Motivated by the exceptionally generalized geometry…
Materials with interesting physical properties are often designed based on our understanding of the target physical effects. The physical properties can be either explicitly observed ("apparent") or concealed by the perceived symmetry…
Real Clifford algebras for arbitrary number of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real,…
This paper contains a review of the theoretical foundations of Clifford algebras, spinors and spinor bundles in the so-called co-frame formalism. A compact index-free notation is introduced, along with a series of identities useful for…