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Equivariant surgery with middle dimensional singular sets. II: Equivariant framed cobordism invariance

机译:具有中等维数奇异集的等变手术。 II:等变框架式Cobordism不变性

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Let G be a finite group and let f : X --> Y be a degree 1, G-framed map such that X and Y are simply connected, closed, oriented, smooth manifolds of dimension n = 2k greater than or equal to 6 and such that the dimension of the singular set of the G-space X is at most k. In the previous article, assuming f is k-connected, we defined the G-equivariant surgery obstruction sigma (f) in a certain abelian group. There it was shown that if sigma (f) = 0 then f is G-framed cobordant to a homotopy equivalence f' : X' --> Y. In the present article, we prove that the obstruction sigma (f) is a G-framed cobordism invariant. Consequently, the G-surgery obstruction sigma (f) is uniquely associated to f : X --> Y above even if it is not k-connected. [References: 10]
机译:令G为有限群,令f:X-> Y为1度,G框架图,使得X和Y简单连接,闭合,定向且光滑的流形,尺寸n = 2k大于或等于6 G空间X的奇异集合的维数最大为k。在上一篇文章中,假设f是k连接的,我们在某个阿贝尔群中定义了G等距手术梗阻sigma(f)。结果表明,如果sigma(f)= 0,那么f是同构对等价f':X'-> Y的G构架同构。在本文中,我们证明了阻塞sigma(f)是G框架的cobordism不变量。因此,即使不进行k连接,G手术梗阻sigma(f)仍与上面的f:X-> Y唯一相关。 [参考:10]

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