We introduce an invariant of tuples of commuting diffeomorphisms on a 4‐manifold using families of Seiberg–Witten equations. This is a generalization of Ruberman's invariant of diffeomorphisms defined using 1‐parameter families of Seiberg–Witten equations. Our invariant yields an application to the homotopy groups of the space of positive scalar curvature metrics on a 4‐manifold. We also study the extension problem for families of 4‐manifolds using our invariant.

中文翻译：

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Seiberg-Witten方程的正标量曲率和高维族

我们使用Seiberg-Witten方程族介绍了4流形上的通勤微分元组的不变性。这是使用Seiberg-Witten方程的1参数族定义的Ruberman微分形不变性的推广。我们的不变量将应用应用于4流形上正标量曲率度量空间的同伦组。我们还使用不变式研究了4流形族的扩展问题。