Grigori Avramidi

activity

20112026

most citedMod

p

and torsion homology growth in nonpositive curvature

13 citations · 37 across the 17 of their papers we have counts for

collaborators

21 papers

math.GT2026

Reflections on branched covers

Grigori Avramidi, Boris Okun, Kevin Schreve

A flag complex $L$ determines a locally CAT(0) cube complex $P_{L}$ with the links of all vertices isomorphic to $L$ . The fundamental group of $P_{L}$ is the commutator subgroup of the…

math.GT2026

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 $p : M^{d} \to R^{m}$ , where $M^{d}$ is a closed hyperbolic manifold of large injec…

math.AT2026

L^2-Betti numbers in prime characteristic and a conjecture of Wise

Grigori Avramidi, Wolfgang Lueck

We systematically study L^2-Betti numbers in zero and prime characteristic and apply them to a conjecture of Wise stating that all towers of a finite 2-complex are non-positive if…

math.GT2024

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…

math.GT2024

Edge subdivisions and the $L^{2}$ -homology of right-angled Coxeter groups

Grigori Avramidi, Boris Okun, Kevin Schreve

If $L$ is a flag triangulation of $S^{n - 1}$ , then the Davis complex $Σ_{L}$ for the associated right-angled Coxeter group $W_{L}$ is a contractible $n$ -manifold. A special case of a co…

math.GT2023

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…

math.GT2023★ 1 cited

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…

math.GT2021★ 1 cited

Fungible obstructions to embedding 2-complexes

Grigori Avramidi, T. Tam Nguyen Phan

We give examples of finite, simplicial $2$ -complexes that do not PL embed in $R^{4}$ and exhibit, for each such complex, a family of PL immersions into $R^{4}$ that h…

math.GT2021

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 $2$ -complexes with surface fundamental groups are standard. We also give an…

math.GR2020★ 13 cited

Mod $p$ and torsion homology growth in nonpositive curvature

Grigori Avramidi, Boris Okun, Kevin Schreve

We compute the mod $p$ homology growth of residual sequences of finite index normal subgroups of right-angled Artin groups. We find examples where this differs from the rational ho…

math.GT2017★ 1 cited

Examples of noncompact nonpositively curved manifolds

Grigori Avramidi, T. Tam Nguyen Phan

We give a simple construction of new, complete, finite volume manifolds $M$ of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetr…

math.GT2017

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…

math.GT2016

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 $n$ -manifolds $M$ of bounde…

math.GT2015★ 1 cited

Ends of finite volume, nonpositively curved manifolds

Grigori Avramidi

We study complete, finite volume $n$ -manifolds $M$ of bounded nonpositive sectional curvature. A classical theorem of Gromov says that if such $M$ has negative curvature then it is…

math.GT2015★ 3 cited

Rational manifold models for duality groups

Grigori Avramidi

We show that a finite type duality group of dimension $d > 2$ is the fundamental group of a $(d + 3)$ -manifold with rationally acyclic universal cover. We use this to find closed manif…

math.GT2014★ 12 cited

The action dimension of right-angled Artin groups

Grigori Avramidi, Michael W. Davis, Boris Okun +1

The action dimension of a discrete group $Γ$ is the smallest dimension of a contractible manifold which admits a proper action of $Γ$ . Associated to any flag complex $L$ there is a…

math.DG2013

Horospherical limit points of locally symmetric spaces

Grigori Avramidi, Dave Witte Morris

Suppose X/Gamma is an arithmetic locally symmetric space of noncompact type (with the natural metric induced by the Killing form of the isometry group of X), and let p be a point o…

math.GT2013

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 $M$ with sectional curvature $- 1 < K < 0$ . We prove that $π_{1} M$ cannot be a 3-manifold group. A classical theorem…

math.GT2012★ 4 cited

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…

math.GT2011

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 $\geq 3$ , no metric $g$ has more symmetry than the locally symmetr…

math.GT2011★ 1 cited

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…

Reflections on branched covers

Cellular waists of hyperbolic spaces

L^2-Betti numbers in prime characteristic and a conjecture of Wise

L^2-Betti numbers of branched covers of hyperbolic manifolds

Edge subdivisions and the L2-homology of right-angled Coxeter groups

Group rings and hyperbolic geometry

Homology growth, hyperbolization, and fibering

Fungible obstructions to embedding 2-complexes

Division in group rings of surface groups

Mod p and torsion homology growth in nonpositive curvature

Examples of noncompact nonpositively curved manifolds

Incompressible fillings of manifolds

Half dimensional collapse of ends of manifolds of nonpositive curvature

Ends of finite volume, nonpositively curved manifolds

Rational manifold models for duality groups

The action dimension of right-angled Artin groups

Horospherical limit points of locally symmetric spaces

Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups

Flat cycles in the homology of Γ\SL(m,R)/SO(m)

Periodic flats and group actions on locally symmetric spaces

Smith theory, L2 cohomology, isometries of locally symmetric manifolds and moduli spaces of curves

Edge subdivisions and the $L^{2}$ -homology of right-angled Coxeter groups

Mod $p$ and torsion homology growth in nonpositive curvature