论文标题
在三个manifold小组的代数K理论上
On the algebraic K-theory of 3-manifold groups
论文作者
论文摘要
我们提供了Whitehead团体的描述，以及代数$ K $ Theory群体，即与其有限亚组的Whitehead组和某些NIL组的Whitehead小组有关的连接，定向，封闭的$ 3 $ manifold的基本组。我们使用的主要工具是：K-Theoretic Farrell-Jones同构猜想，为三个manifold群体中虚拟循环亚组的通用空间的模型构建，以及Prime和JSJ解释以及众所周知的几何学定理。
We provide descriptions of the Whitehead groups, and the algebraic $K$-theory groups, of the fundamental group of a connected, oriented, closed $3$-manifold in terms of Whitehead groups of their finite subgroups and certain Nil-groups. The main tools we use are: the K-theoretic Farrell-Jones isomorphism conjecture, the construction of models for the universal space for the family of virtually cyclic subgroups in 3-manifold groups, and both the prime and JSJ-decompositions together with the well-known geometrization theorem.
