Covering and gluing of algebras and differential algebras

The contraction of $SU_μ(2)$ and its differential structures to $E_κ(2)$

The deformed double covering of E(2) group, denoted by $\tilde{E}_κ(2)$, is obtained by contraction from the $SU_μ(2)$. The contraction procedure is then used for producing a new examples of differential calculi: 3D-left covariant calculus on both $\tilde{E}_κ(2)$ and the deformed Euclidean group $E_κ(2)$ and two different 4D-bicovariant calculi on $\tilde{E}_κ(2)$ which correspond to the one 4D-bicovariant calculi on $E_κ(2)$ described in Ref.\cite{b14}.

On the algebra of cornered Floer homology

Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2-algebra, the nilCoxeter sequential 2-algebra, and to a surface with connected boundary an algebra-module over this 2-algebra, such that a natural gluing property is satisfied. Moreover, with a view toward the structure of a potential Floer homology theory of 3-manifolds with codimension-two corners, we present a decomposition theorem for the Floer complex of a plan…

量子化覆盖的非交换几何

Noncommutative Geometry of Quantized Coverings

本文提出一个统一的公理化理论，涵盖多种$C^*$-代数覆盖，并推广万有覆盖、基本群等几何构造，给出纯代数证明。