Assume that \(M({{\mathcal {T}}})\) is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph \(\mathcal {T}\). We consider the combinatorial multivariable Poincaré series associated with \(\mathcal {T}\) and its counting functions, which encode rich topological information. Using the ‘periodic constant’ of the series (with reduced variables associated with an arbitrary subset \({{\mathcal {I}}}\) of the set of vertices) we prove surgery formulae for the normalized Seiberg–Witten invariants: the periodic constant associated with \({{\mathcal {I}}}\) appears as the difference of the Seiberg–Witten invariants of \(M({{\mathcal {T}}})\) and \(M({{\mathcal {T}}}{\setminus }{{\mathcal {I}}})\) for any \({{\mathcal {I}}}\).

中文翻译：

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垂线3流形的Seiberg-Witten不变量的手术公式

假设\（M（{{\ mathcal {T}}}）\）是与连接的负定图\（\ mathcal {T} \）相关的有理同源性球体垂直3流形。我们考虑与\（\ mathcal {T} \）相关联的组合多变量Poincaré级数及其计数功能，它们编码丰富的拓扑信息。利用该系列的“周期常数”（具有与该组顶点的任意子集\（{{\ mathcal {I}}} \\相关的减少的变量），我们证明了归一化的Seiberg-Witten不变量的手术公式：与\（{{\ mathcal {I}}} \\）相关的周期常数出现为\（M（{{\ mathcal {T}}}）\）的Seiberg–Witten不变量的差，并且\（M（{{\ mathcal {T}}} {\ setminus} {{\ mathcal {I}}}）\）对于任何\（{{mathcal {I}}}} \）。