974 research outputs found
Farrell-Jones Conjecture for fundamental groups of graphs of virtually cyclic groups
In this note, we prove the K- and L-theoretic Farrell-Jones Conjecture with
coefficients in an additive category for fundamental groups of graphs of
virtually cyclic groups.Comment: Added more details in section 3. Many other small change
On the finiteness of the classifying space for the family of virtually cyclic subgroups
Given a group G, we consider its classifying space for the family of
virtually cyclic subgroups. We show for many groups, including for example,
one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and
CAT(0) cube groups, that they do not admit a finite model for this classifying
space unless they are virtually cyclic. This settles a conjecture due to
Juan-Pineda and Leary for these classes of groups.Comment: Minor changes, to appear in Groups, Geometry, and Dynamic
Finiteness properties for relatives of braided Higman--Thompson groups
We study the finiteness properties of the braided Higman--Thompson group
with labels in , and and
with labels in where is the braid group with strings and
is its pure braid subgroup. We show that for all and , the group (resp. or ) is of type
if and only if is. Our result in particular confirms a recent
conjecture of Aroca and Cumplido.Comment: 25 pages;first part of arXiv:2103.14589v1 with the second part to
appear separatel
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