We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an orientable surface with respect to its antipodal involution. Our estimates are at most one unit from being optimal, and are closely related to the (regular) topological complexity of non-orientable surfaces.

中文翻译：

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可定向表面群的有效拓扑复杂性

我们使用重写系统来拼写表面组产品的（扭曲）同调组中的杯子产品。这使我们能够从可定向表面相对于其对映对合的有效拓扑复杂性下方检测出非平凡的障碍边界。我们的估计最多是最佳状态的一个单位，并且与不可定向曲面的（规则）拓扑复杂性密切相关。