## Coarse coherence of metric spaces and groups and its permanence properties. (arXiv:1804.00944v2 [math.KT] UPDATED)

We introduce properties of metric spaces and, specifically, finitely
generated groups with word metrics which we call coarse coherence and coarse
regular coherence. They are geometric counterparts of the classical algebraic
notion of coherence and the regular coherence property of groups defined and
studied by F. Waldhausen. The new properties can be defined in the general
context of coarse metric geometry and are coarse invariants. In particular,
they are quasi-isometry invariants of spaces and groups.
We show that coarse regular coherence implies weak regular coherence, a
weakening of regular coherence by G. Carlsson and the first author. The latter
was introduced with the same goal as Waldhausen's, in order to perform
computations of algebraic K-theory of group rings. However, all groups known to
be weakly regular coherent are also coarsely regular coherent. The new
framework allows us to prove structural results by developing permanence
properties, including the particularly import查看全文