We prove that Manolescu and Woodward's Symplectic Instanton homology, and its twisted versions are natural, and define maps associated to four dimensional cobordisms within this theory. This allows one to define representations of the mapping class group and the fundamental group of a 3-manifold, and to have a geometric interpretation of the maps appearing in the long exact sequence for symplectic instanton homology, together with vanishing criterions.

中文翻译：

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辛瞬间子同源性：自然性和来自协边的映射

我们证明了 Manolescu 和 Woodward 的辛瞬间同调及其扭曲版本是自然的，并在该理论中定义了与四维坐标相关的映射。这允许定义映射类群和 3-流形的基本群的表示，并且对出现在辛瞬时子同源性的长精确序列中的映射以及消失准则进行几何解释。