二维局部Z_2-系统与不可定向闭曲面

Two dimensional local Z_2-systems and non-orientable closed surfaces

用多面体构造流形(代数簇)是环簇理论中的一个经典技巧.通过局部Z_2-系统我们可以将这种构造推广到实流形上.在本文中,作者给出了这类流形的欧拉数的计算公式,并证明了所有的不可定向闭曲面都可以由二维局部Z_2-系统来实现.

It is a canonical technique to construct manifolds （algebraic varieties） from polytopes in the theory of toric variety. We can generalize this construction to real manifolds via local Z2-systems. In this paper, the authors give the formula of Euler numbers of these manifolds, and show that all non-orientable closed surfaces can be realized from two dimensional local Z2-systems.