Poincare对偶性和周期性，II .詹姆斯周期
Poincare duality and Periodicity, II. James Periodicity
摘要：
设K是一个连通的有限复形。本文研究了是否可以将一个胞元附加到某个迭代悬置S^j K上，使所得空间满足Poincare对偶性的问题。当这是可能的，我们说S^j K是一个脊椎。我们引入了二次自对偶的概念，并证明了如果K是二次自对偶，则S^j K是一个刺，只要j是一个合适的2的幂。2的幂来自詹姆斯周期定理。我们简要地解释我们的主要结果，考虑到bordism，给出了一个新的解释的四倍周期性的手术梗阻组。由此得到了James周期性与L-理论中的四重周期性之间的关系。
英文摘要：
Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension S^j K so that the resulting space satisfies Poincare duality. When this is possible, we say that S^j K is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then S^j K is a spine whenever j is a suitable power of two. The powers of two come from the James periodicity theorem. We briefly explain how our main results, considered up to bordism, give a new interpretation of the four-fold periodicity of the surgery obstruction groups. We therefore obtain a relationship between James periodicity and the four-fold periodicity in L-theory.
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