arXiv subjects

Man Chuen Cheng

Publications and source records attributed to Man Chuen Cheng.

3 recordsLinked to original sources

arXiv2019

On the moduli spaces of commuting elements in the projective unitary groups

We provide descriptions for the moduli spaces $\text{Rep}(Γ, PU(m))$, where $Γ$ is any finitely generated abelian group and $PU(m)$ is the group of $m\times m$ projective unitary matrices. As an application we show that for any connected CW-complex $X$ with $π_1(X)\cong \mathbf{Z}^n$, the natural map $π_0(\text{Rep}(π_1(X), PU(m)))\to [X, BPU(m)]$ is injective, hence providing a complete enumeration of the isomorphism classes of flat principal $PU(m)$-bundles over $X$.

math.RT↗

arXiv2016

Representation spaces for central extensions and almost commuting unitary matrices

Let $Γ$ denote a central extension of the form $1\to \mathbb{Z}^r\toΓ\to \mathbb{Z}^n\to 1$. In this paper we describe the topology of the spaces of homomorphisms $\text{Hom}(Γ, U(m))$ and the associated moduli spaces $\text{Rep}(Γ, U(m))$, where $U(m)$ is the group of $m\times m$ unitary matrices.

math.AT↗

arXiv2013

Poincare duality in Morava K-theory for classifying spaces of orbifolds

Greenlees and Sadofsky showed that the classifying spaces of finite groups are self-dual with respect to Morava K-theory K(n). Their duality map was constructed using a transfer map. We generalize their duality map and prove a K(n)-version of Poincare duality for classifying spaces of orbifolds. By regarding these classifying spaces as the homotopy types of certain differentiable stacks, our construction can be viewed as a stack version of Spanier-Whitehead type construction. Some examples and calculations will be given at the end.

math.AT↗