2,799 research outputs found
Graphical small cancellation groups with the Haagerup property
We prove the Haagerup property (= Gromov's a-T-menability) for finitely
generated groups defined by infinite presentations satisfying the graphical
C'(lambda)-small cancellation condition with respect to graphs endowed with a
compatible wall structure. We deduce that these groups are coarsely embeddable
into a Hilbert space and that the strong Baum-Connes conjecture and, hence, the
Baum-Connes conjecture with arbitrary coefficients hold for them. As the main
step we show that C'(lambda)-complexes satisfy the linear separation property.
Our result provides many new examples and a general technique to show the
Haagerup property for graphical small cancellation groups.Comment: 29 pages, minor modifications to v
Braids, posets and orthoschemes
In this article we study the curvature properties of the order complex of a
graded poset under a metric that we call the ``orthoscheme metric''. In
addition to other results, we characterize which rank 4 posets have CAT(0)
orthoscheme complexes and by applying this theorem to standard posets and
complexes associated with four-generator Artin groups, we are able to show that
the 5-string braid group is the fundamental group of a compact nonpositively
curved space.Comment: 33 pages, 16 figure
Groups of type via graphical small cancellation
We construct an uncountable family of groups of type . In contrast to
every previous construction of non-finitely presented groups of type we do
not use Morse theory on cubical complexes; instead we use Gromov's graphical
small cancellation theory.Comment: 3 figures. Second version: two paragraphs added emphasizing the
difference between our construction and Morse theoretic one
- …