The Algebraic Theory of Surgery I. Foundations
The Algebraic Theory of Surgery I. Foundations
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外科代数理论 I. 基础
DOI：
10.1112/plms/s3-40.1.87
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发表时间：
1980
影响因子：
1.8
通讯作者：
A. Ranicki
中科院分区：
文献类型：
--
作者：
A. Ranicki
代数。带对合环a上的n维代数庞加莱复：a -+ aar + a是具有n维庞加莱对偶H*(G) = Hn_*(G)的a模链复形G。我们将使用n维代数庞加莱复形定义两个协变函子Ln {Ln}序列：（带对合的环）-+（阿贝尔群）（n E Z）。使得LO(A){分别LO(A)}为A上非奇异对称{二次}形式的Witt群，二次l群Ln(A)即为Wall[25]的手术梗阻群，其周期为4
algebra. An n-dimensional algebraic Poincare complex over a ring A with an involution -: A -+ A; a r+ a is an A-module chain complex G with an n-dimensional Poincare duality H*(G) = Hn_*(G). We shall use n-dimensional algebraic Poincare complexes to define two sequences of covariant functors Ln {Ln}: (rings with involution) -+ (abelian groups) (n E Z) . such that LO(A) {respectively Lo(A)} is the Witt group of non-singular symmetric {quadratic} forms over A. The quadratic L-groups Ln(A) will turn out to be the surgery obstruction groups of Wall [25], with a 4-periodicity