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arXiv · 2011.11811

On the algebraic K-theory of 3-manifold groups

Daniel Juan-Pineda·Luis Jorge Sánchez Saldaña
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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.

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BibTeXRIS

Daniel Juan-Pineda, Luis Jorge Sánchez Saldaña. 2020-11-24. On the algebraic K-theory of 3-manifold groups. https://arxiv.org/abs/2011.11811

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