Type: Article

On the algebraic K-theory of orientable 3-manifold groups

Juan-Pineda, Daniel; Sánchez Saldaña, Luis Jorge;

Abstract:

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.