# The Cohomology Invariant for Class DIII Topological Insulators

@article{DeNittis2021TheCI, title={The Cohomology Invariant for Class DIII Topological Insulators}, author={Giuseppe De Nittis and Kyonori Gomi}, journal={Annales Henri Poincar{\'e}}, year={2021}, volume={23}, pages={3587 - 3632} }

This work concerns the description of the topological phases of band insulators of class DIII by using the equivariant cohomology. The main result is the definition of a cohomology class for general systems of class DIII which generalizes the well-known Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_2…

## 2 Citations

### A new light on the FKMM invariant and its consequences

- Mathematics
- 2022

A BSTRACT . “Quaternionic” vector bundles are the objects which describe the topological phases of quantum systems subjected to an odd time-reversal symmetry (class AII). In this work we prove that…

### Symmetric Fermi projections and Kitaev’s table: Topological phases of matter in low dimensions

- Physics, MathematicsJournal of Mathematical Physics
- 2022

We review Kitaev’s celebrated “periodic table” for topological phases of condensed matter, which identifies ground states (Fermi projections) of gapped periodic quantum systems up to continuous…

## References

SHOWING 1-10 OF 53 REFERENCES

### Homotopy theory of strong and weak topological insulators

- Mathematics, Physics
- 2015

We use homotopy theory to extend the notion of strong and weak topological insulators to the non-stable regime (low numbers of occupied/empty energy bands). We show that for strong topological…

### Generalized Connes-Chern characters in KK-theory with an application to weak invariants of topological insulators

- Mathematics
- 2016

We use constructive bounded Kasparov K-theory to investigate the numerical invariants stemming from the internal Kasparov products $K_i(\mathcal A) \times KK^i(\mathcal A, \mathcal B) \rightarrow…

### Chiral vector bundles

- Mathematics
- 2010

Given a smooth $G$-vector bundle $E \to M$ with a connection $\nabla$, we propose the construction of a sheaf of vertex algebras $\mathcal{E}^{ch(E,\nabla)}$, which we call a \textit{chiral vector…

### CLASSIFICATION OF "REAL" BLOCH-BUNDLES: TOPOLOGICAL INSULATORS OF TYPE AI

- Mathematics, Computer Science
- 2014

A classification of type AI topological insulators in dimension d = 1; 2; 3; 4 which is based on the equivariant homotopy properties of "Real" vector bundles is provided, able to take care also of the unstable regime which is usually not accessible via K-theoretical techniques.

### Classification of “Quaternionic" Bloch-Bundles

- Mathematics
- 2015

We provide a classification of type AII topological quantum systems in dimension d = 1, 2, 3, 4. Our analysis is based on the construction of a topological invariant, the FKMM-invariant, which…

### Controlled Topological Phases and Bulk-edge Correspondence

- Mathematics
- 2015

In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with…

### Bott Periodicity for $${\mathbb{Z}_2}$$Z2 Symmetric Ground States of Gapped Free-Fermion Systems

- Physics, Mathematics
- 2014

Building on the symmetry classification of disordered fermions, we give a proof of the proposal by Kitaev, and others, for a “Bott clock” topological classification of free-fermion ground states of…

### Topological invariant for generic one-dimensional time-reversal-symmetric superconductors in class DIII

- Physics
- 2013

A one-dimensional time-reversal-symmetric topological superconductor (symmetry class DIII) features a single Kramers pair of Majorana bound states at each of its ends. These holographic…