2020/11/24 by Daniel Juan-Pineda, Juan-Pineda, Daniel, Luis Jorge Sánchez Saldaña +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.2011.11811
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.