Tom Stoiber
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View article: The role of self-adjoint extensions in the bulk-edge correspondence
The role of self-adjoint extensions in the bulk-edge correspondence Open
We investigate the role of self-adjoint extensions in the bulk-edge correspondence for topological insulators. While the correspondence is well understood in discrete models with spectral gaps, complications arise in the presence of unboun…
View article: Spectral continuity for étale groupoids with the Rapid decay property
Spectral continuity for étale groupoids with the Rapid decay property Open
We show that the reduced groupoid C*-algebras of continuous fields of étale groupoids satisfying the rapid decay property yield continuous fields of C*-algebras. This establishes a new sufficient criterion that applies in the non-amenable …
View article: Invariant measures on the transversal hull of cone semigroups and some applications
Invariant measures on the transversal hull of cone semigroups and some applications Open
Let $\LL_{\bf v}\subset \Z^D$ be a suitable cone semigroup and $\A_{\bf v}$ its reduced semigroup $C^*$-algebra. In this paper, we compute the $\LL_{\bf v}$-invariant measures in the transversal hull of the semigroup $\LL_{\bf v}$ that exh…
View article: On Frustration-Free Quantum Spin Models
On Frustration-Free Quantum Spin Models Open
The goal of our work is to characterize the landscape of the frustration-free quantum spin models over the Cayley graph of a finitely generated group $G$. This is achieved by establishing $G$-equivariant morphisms from the partially ordere…
View article: A space-adiabatic approach for bulk-defect correspondences in lattice models of topological insulators
A space-adiabatic approach for bulk-defect correspondences in lattice models of topological insulators Open
In space-adiabatic approaches one can approximate Hamiltonians that are modulated slowly in space by phase-space functions that depend on position and momentum. In this paper, we establish a rigorous relation between this approach and the …
View article: A spectral localizer approach to strong topological invariants in the mobility gap regime
A spectral localizer approach to strong topological invariants in the mobility gap regime Open
Topological phases of gapped one-particle Hamiltonians with (anti)-unitary symmetries are classified by strong topological invariants according to the Altland-Zirnbauer table. Those indices are still well-defined in the regime of strong di…
View article: C*-framework for higher-order bulk-boundary correspondences
C*-framework for higher-order bulk-boundary correspondences Open
A typical crystal is a finite piece of a material which may be invariant under some point symmetry group. If it is a so-called intrinsic higher-order topological insulator or superconductor, then it displays boundary modes at hinges or cor…
View article: The generators of the K-groups of the sphere
The generators of the K-groups of the sphere Open
This note presents an elementary iterative construction of the generators for the complex $K$-groups $K_i(C(\SM^d))$ of the $d$-dimensional spheres. These generators are explicitly given as the restrictions of Dirac or Weyl Hamiltonians to…
View article: Callias-type operators associated to spectral triples
Callias-type operators associated to spectral triples Open
Callias-type (or Dirac-Schrödinger) operators associated to abstract semifinite spectral triples are introduced and their indices are computed in terms of an associated index pairing derived from the spectral triple. The result is then int…
View article: Topological Spectral Bands with Frieze Groups
Topological Spectral Bands with Frieze Groups Open
Frieze groups are discrete subgroups of the full group of isometries of a flat strip. We investigate here the dynamics of specific architected materials generated by acting with a frieze group on a collection of self-coupling seed resonato…
View article: Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems
Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems Open
This monograph develops the theory of Besov spaces for abelian group actions on semifinite von Neumann algebras and then proves Peller criteria for traceclass properties of associated Hankel operators. This allows to extend known index the…
View article: Spectral localization for semimetals and Callias operators
Spectral localization for semimetals and Callias operators Open
A semiclassical argument is used to show that the low-lying spectrum of a selfadjoint operator, the so-called spectral localizer, determines the number of Dirac or Weyl points of an ideal semimetal. Apart from the IMS localization procedur…
View article: Invariants of disordered semimetals via the spectral localizer
Invariants of disordered semimetals via the spectral localizer Open
The spectral localizer consists of placing the Hamiltonian in a Dirac trap. For topological insulators its spectral asymmetry is equal to the topological invariants, providing a highly efficient tool for numerical computation. Here this te…
View article: Callias-type operators associated to spectral triples
Callias-type operators associated to spectral triples Open
Callias-type (or Dirac-Schrödinger) operators associated to abstract semifinite spectral triples are introduced and their indices are computed in terms of an associated index pairing derived from the spectral triple. The result is then int…
View article: Invariants of disordered semimetals via the spectral localizer
Invariants of disordered semimetals via the spectral localizer Open
The spectral localizer consists in placing the Hamiltonian in a Dirac trap. For topological insulators its spectral asymmetry is equal to the topological invariants, providing a highly efficient tool for numerical computation. Here this te…
View article: The spectral localizer for semifinite spectral triples
The spectral localizer for semifinite spectral triples Open
The notion of a spectral localizer is extended to pairings with semifinite spectral triples. By a spectral flow argument, any semifinite index pairing is shown to be equal to the signature of the spectral localizer. As an application, a fo…