A non-extended hermitian form over ℤ[ℤ]
A non-extended hermitian form over ℤ[ℤ]
复制标题
ℤ[ℤ] 上的非扩展埃尔米特形式
DOI：
10.1007/bf02677483
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发表时间：
1997
影响因子：
0.6
通讯作者：
P. Teichner
中科院分区：
文献类型：
--
作者：
I. Hambleton;P. Teichner
本文描述了群环Z[Z]上秩为4的非奇异厄米特形式，它不是由整数扩张的。此外，我们证明了在某些不定假设下，自由Z[Z]模上的每个非奇异埃尔米特形式都是由整数扩张而来的。作为推论，存在一个具有基本群Z的闭定向四维流形，它不是S × S与一个单连通四维流形的连通和.
We describe a nonsingular hermitian form of rank 4 over the group ring Z[Z] which is not extended from the integers. Moreover, we show that under certain indefiniteness asumptions, every nonsingular hermitian form on a free Z[Z]module is extended from the integers. As a corollary, there exists a closed oriented 4-dimensional manifold with fundamental group Z which is not the connected sum of S × S with a simply-connected 4-manifold.