228 research outputs found
Density of isoperimetric spectra
We show that the set of k-dimensional isoperimetric exponents of finitely
presented groups is dense in the interval [1, \infty) for k > 1. Hence there is
no higher-dimensional analogue of Gromov's gap (1,2) in the isoperimetric
spectrum.Comment: 34 pages, 3 figure
Morse theory and conjugacy classes of finite subgroups
We construct a CAT(0) group containing a finitely presented subgroup with
infinitely many conjugacy classes of finite-order elements. Unlike previous
examples (which were based on right-angled Artin groups) our ambient CAT(0)
group does not contain any rank 3 free abelian subgroups.
We also construct examples of groups of type F_n inside mapping class groups,
Aut(F), and Out(F) which have infinitely many conjugacy classes of finite-order
elements.Comment: 10 pages, 4 figure
Morse theory and conjugacy classes of finite subgroups II
We construct a hyperbolic group with a finitely presented subgroup, which has
infinitely many conjugacy classes of finite-order elements.
We also use a version of Morse theory with high dimensional horizontal cells
and use handle cancellation arguments to produce other examples of subgroups of
CAT(0) groups with infinitely many conjugacy classes of finite-order elements.Comment: 18 pages, 7 figure
American Architecture 2
Review of guide to American Architecture book by David P. Handli
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