Domain walls between different topological phases are one of the most interesting phenomena that reveal non-trivial bulk properties phases. Very recently, gapped domain have been intensively studied. In this paper, we systematically construct a large class lattice models for gapless twisted and untwisted gauge theories with arbitrary finite group $G$. As simple examples, numerically study sever...

A quandle is an algebraic system with a binary operation satisfying three axioms modelled on the Reidemeister moves of planar diagrams links in 3-space. The paper establishes new relationship between cohomology, extensions and automorphisms quandles. We derive four term exact sequence relating 1-cocycles, second cohomology certain group abelian extension non-abelian counterpart this involving d...

We discuss the topological properties of a two-dimensional free Abelian gauge theory in the framework of BRST cohomology. We derive the conserved and nilpotent BRST and co-BRST charges and express the Hodge decomposition theorem in terms of these charges and the Laplacian operator. It is because of the topological nature of the free U(1) gauge theory that the Laplacian operator goes to zero whe...

For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new cohomology to construct a Serre spectral sequence for equivariant fibrations. Bredon [1] introduced what is now called Bredon cohomology, with the purpose of developing obstruction theory in the context of ...

Generalizing a result of Depauw, we prove that the geometric cohomology groups for a Z d action are in any dimension isomorphic to the Feldman-Moore cohomology groups rsp. the algebraic group cohomology groups. This result holds in the smooth, topological or measurable category and for general Polish groups as coeecient groups.

We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...

We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...