Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1892894 | Journal of Geometry and Physics | 2013 | 7 Pages |
Abstract
We formulate a condition for the existence of a SpinCSpinC-structure on an oriented flat manifold MnMn with H2(Mn,R)=0H2(Mn,R)=0. We prove that MnMn has a SpinCSpinC-structure if and only if there exists a homomorphism ϵ:π1(Mn)→SpinC(n)ϵ:π1(Mn)→SpinC(n) such that λ̄n∘ϵ=h, where h:π1(Mn)→SO(n)h:π1(Mn)→SO(n) is a holonomy homomorphism and λ̄n:SpinC(n)→SO(n) is a standard homomorphism defined. As an application we shall prove that all cyclic Hantzsche–Wendt manifolds do not have the SpinCSpinC-structure.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
A. Ga̧sior, A. Szczepański,