V. GRADINARU AND R. HIPTMAIR † Abstract. Conforming finite elements inH(div; Ω) andH(curl; Ω) can be regarded as discrete differential forms (Whitney–forms). The construction of such forms is based on an interpolation idea, which boils down to a simple extension of the differential form to the interior of elements. This flexible approach can accommodate elements of more complicated shapes than ...

Let $(M,g)$ be a pseudo-Riemannian manifold of signature $(p,q)$. We compute the obstruction for vector bundle $S$ over to admit Dirac operator whose principal symbol induces on structure irreducible real Clifford modules complex type, that is, spinor type. In order do this, we use theory Lipschitz structures in $p-q\equiv_8 3,7$ reformulate problem as $\mathrm{Spin}^{o}_{\alpha}$ with $\alpha ...

The first section of this paper defines and studies a graded ring K . F associated to any field F. By definition, K~F is the target group of the universal n-linear function from F ~ x ... • F ~ to an additive group, satisfying the condition that al • " ' x a, should map to zero whenever a i -q-a i + ~ = 1. Here F ~ denotes the multiplicative group F 0 . Section 2 constructs a homomorphism ~: K,...

Let Γ be the fundamental group of the complement of a K(Γ, 1) hyperplane arrangement (such as Artin’s pure braid group) or more generally a homologically toroidal group as defined below. The subgroup of elements in the complex K-theory of BΓ which arises from complex unitary representations of Γ is shown to be trivial. In the case of real K-theory, this subgroup is an elementary abelian 2-group...

Abstract Higher-order topological insulators have been introduced in the precursory Benalcazar-Bernevig-Hughes quadrupole model, but no electronic compound has proposed to be a insulator (QTI) yet. In this work, we predict that Ta 2 M 3 Te 5 ( = Pd, Ni) monolayers can 2D QTIs with second-order topology due double-band inversion. A time-reversal-invariant system two mirror reflections (M x and y...