Topological Hopf-Chern insulators and the Hopf superconductor

Chern Character, Hopf Algebras, and Brs Cohomology

We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological algebras introduced in a previous paper [35], based on Quillen superconnections and heat-kernel regularization. Then we adapt the formalism to the cyclic coh...

Some Characterizations of Hopf Group on Fuzzy Topological Spaces

In this paper, some fundamental concepts are given relating to fuzzytopological spaces. Then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. Also the fuzzy topological spaces which are Hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...

Hopf instantons in Chern–Simons theory

We study an Abelian Chern–Simons & Fermion system in three dimensions. In the presence of a fixed prescribed background magnetic field we find an infinite number of fully three-dimensional solutions. These solutions are related to Hopf maps and are, therefore, labelled by the Hopf index. Further we discuss the interpretation of the background field. )email address: [email protected], [email protected]...

The Hopf Extension Theorem for Topological Spaces

The Z2 classification of dimensional reduced Hopf insulators.

Hopf insulators are characterized by a topological invariant called the Hopf index which classifies maps from three-sphere to two-sphere, instead of a Chern number or a Chern parity. In contrast to a topological insulator, the Hopf insulator is not protected by any kind of symmetry. By dimensional reduction, we argue that there exists a new type of Z(2) index for 2D Hamiltonian with a vanishing...