21 citations · 98 across the 26 of their papers we have counts for
13 papers · 1 filter
Filling functions of arithmetic groups
Enrico Leuzinger, Robert Young
The Dehn function and its higher-dimensional generalizations measure the difficulty of filling a sphere in a space by a ball. In nonpositively curved spaces, one can construct fill…
The distortion dimension of --rank lattices
Enrico Leuzinger, Robert Young
Let be a symmetric space of noncompact type and rank . We prove that horospheres in are Lipschitz --connected if their centers are not contained in a pro…
Homological and homotopical Dehn functions are different
Aaron Abrams, Noel Brady, Pallavi Dani +1
The homological and homotopical Dehn functions are different ways of measuring the difficulty of filling a closed curve inside a group or a space. The homological Dehn function mea…
Filling loops at infinity in the mapping class group
Aaron Abrams, Noel Brady, Pallavi Dani +2
We study the Dehn function at infinity in the mapping class group, finding a polynomial upper bound of degree four. This is the same upper bound that holds for arbitrary right-angl…
High-dimensional fillings in Heisenberg groups
Robert Young
We use intersections with horizontal manifolds to show that high-dimensional cycles in the Heisenberg group can be approximated efficiently by simplicial cycles. This lets us calcu…
Pushing fillings in right-angled Artin groups
Aaron Abrams, Noel Brady, Pallavi Dani +2
We construct "pushing maps" on the cube complexes that model right-angled Artin groups (RAAGs) in order to study filling problems in certain subsets of these cube complexes. We use…