13 citations · 37 across the 17 of their papers we have counts for
18 papers · 1 filter
Reflections on branched covers
Grigori Avramidi, Boris Okun, Kevin Schreve
A flag complex determines a locally CAT(0) cube complex with the links of all vertices isomorphic to . The fundamental group of is the commutator subgroup of the…
Cellular waists of hyperbolic spaces
Grigori Avramidi, Thomas Delzant
We find lower bounds on the topological complexity of fibers of PL and generic smooth maps , where is a closed hyperbolic manifold of large injec…
L^2-Betti numbers of branched covers of hyperbolic manifolds
Grigori Avramidi, Boris Okun, Kevin Schreve
We show that Gromov-Thurston branched covers satisfy the Singer conjecture whenever the degree of the cover is not divisible by a finite set of primes determined by the base manifo…
Edge subdivisions and the -homology of right-angled Coxeter groups
Grigori Avramidi, Boris Okun, Kevin Schreve
If is a flag triangulation of , then the Davis complex for the associated right-angled Coxeter group is a contractible -manifold. A special case of a co…
Group rings and hyperbolic geometry
Grigori Avramidi, Thomas Delzant
For a group acting on a hyperbolic space, we set up an algorithm in the group algebra showing that ideals generated by few elements are free, where few is a function of the minimal…
Homology growth, hyperbolization, and fibering
Grigori Avramidi, Boris Okun, Kevin Schreve
We introduce a hyperbolic reflection group trick which builds closed aspherical manifolds out of compact ones and preserves hyperbolicity, residual finiteness, and -- for almost al…
Fungible obstructions to embedding 2-complexes
Grigori Avramidi, T. Tam Nguyen Phan
We give examples of finite, simplicial -complexes that do not PL embed in and exhibit, for each such complex, a family of PL immersions into that h…
Division in group rings of surface groups
Grigori Avramidi
We prove a division algorithm for group rings of high genus surface groups and use it to show that some -complexes with surface fundamental groups are standard. We also give an…
Examples of noncompact nonpositively curved manifolds
Grigori Avramidi, T. Tam Nguyen Phan
We give a simple construction of new, complete, finite volume manifolds of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetr…
Incompressible fillings of manifolds
Grigori Avramidi
We find boundaries of Borel-Serre compactifications of locally symmetric spaces, for which any filling is incompressible. We prove this result by showing that these boundaries have…
Half dimensional collapse of ends of manifolds of nonpositive curvature
Grigori Avramidi, T. Tam Nguyen Phan
This paper accomplishes two things. First, we construct a geometric analog of the rational Tits building for general noncompact, complete, finite volume -manifolds of bounde…
Ends of finite volume, nonpositively curved manifolds
Grigori Avramidi
We study complete, finite volume -manifolds of bounded nonpositive sectional curvature. A classical theorem of Gromov says that if such has negative curvature then it is…
Rational manifold models for duality groups
Grigori Avramidi
We show that a finite type duality group of dimension is the fundamental group of a -manifold with rationally acyclic universal cover. We use this to find closed manif…
The action dimension of right-angled Artin groups
Grigori Avramidi, Michael W. Davis, Boris Okun +1
The action dimension of a discrete group is the smallest dimension of a contractible manifold which admits a proper action of . Associated to any flag complex there is a…
Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups
Grigori Avramidi, T. Tam Nguyen Phan, Yunhui Wu
We study noncompact, complete, finite volume, Riemannian 4-manifolds with sectional curvature . We prove that cannot be a 3-manifold group. A classical theorem…
Flat cycles in the homology of Γ\SL(m,R)/SO(m)
Grigori Avramidi, T. Tam Nguyen Phan
In this paper we show that flat (m-1)-dimensional tori give nontrivial rational homology cycles in congruence covers of the locally symmetric space SL(m,Z) \SL(m,R)/SO(m). We also…
Periodic flats and group actions on locally symmetric spaces
Grigori Avramidi
We use maximal periodic flats to show that on a finite volume irreducible locally symmetric manifold of dimension , no metric has more symmetry than the locally symmetr…
Smith theory, L2 cohomology, isometries of locally symmetric manifolds and moduli spaces of curves
Grigori Avramidi
We investigate periodic diffeomorphisms of non-compact aspherical manifolds (and orbifolds) and describe a class of spaces that have no homotopically trivial periodic diffeomorphis…