相关论文: On the Obstructions to non-Cliffordian Pin Structu…

In this work we introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction we obtain both…

Using very weak criteria for what may constitute a noncommutative geometry, I show that a pseudo-Riemannian manifold can only be smoothly deformed into noncommutative geometries if certain geometric obstructions vanish. These obstructions…

We study a new class of non-Hermitian topological phases in three dimension in the absence of any symmetry, where the topological robust band degeneracies are Hopf-link exceptional lines. As a concrete example, we investigate the…

Recently, spin splitting of non-relativistic origin in compensated antiferromagnets has drawn growing attention in condensed matter research. Although many materials, now known to exhibit such spin splitting, have been studied for decades,…

States of matter with nontrivial topology have been classified by their bulk symmetry properties. However, by cutting the topological insulator into ribbons, the symmetry of the system is reduced. By constructing effective Hamiltonians…

We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory as well as…

We study the concept of liaison addition for codimension two subschemes of an arithmetically Gorenstein projective scheme. We show how it relates to liaison and biliaison classes of subschemes and use it to investigate the structure of…

It is one of the most important facts in 4-dimensional topology that not every spherical homology class of a 4-manifold can be represented by an embedded sphere. In 1978, M. Freedman and R. Kirby showed that in the simply connected case,…

In this article we provide a more detailed account of the geometry and topology of the composite bundle formalism introduced by Tresguerres in Phys. Rev. D 66 (2002) 064025 [1] to accommodate gravitation as a gauge theory. In the first half…

We define obstructions which obstruct topological pseudo-isotopies from being isotopic to isotopies in dimension four. These match the smooth obstructions of Hatcher-Wagoner for smooth pseudo-isotopies, and accordingly are valued in certain…

In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the…

The classification of emergent spinor fields according to modified bilinear covariants is scrutinized, in spacetimes with nontrivial topology, which induce inequivalent spin structures. Extended Clifford algebras, constructed by equipping…

We report on our investigations concerning algebraic and transcendental Brauer-Manin obstructions to integral points on complements of a hyperplane section in degree four del Pezzo surfaces. We discuss moreover two concepts of an…

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not…

The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new…

In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in $n$…

We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored…

The actions, anomalies, and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond Spin on their worldvolumes. The main examples are twisted String structures. This also extends to…

Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed. A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional…