G. Solomadin

activity

20162026

most citedHow is a graph not like a manifold?

3 citations · 6 across the 17 of their papers we have counts for

collaborators

19 papers

math.AT2026

Cellular approximations for nonsymmetric homotopy operads

Eduardo Hoefel, Grigory Solomadin

In this note, for every topological colored nonsymmetric operad with CW spaces in each arity we construct a homotopy isomorphism with a CW homotopy operad (i.e. all higher homotopi…

math.GT2026

Brieskorn spheres bound orbit spaces of torus manifolds

Grigory Solomadin

We construct a smooth, equivariantly formal, simply connected torus $8$ -manifold over a contractible $4$ -manifold with the boundary a Brieskorn homology $3$ -sphere having a nontriv…

math.AT2026

Almost quaternionic structures on compact rank one symmetric spaces

Oliver Goertsches, Panagiotis Konstantis, Eugenia Loiudice +1

We prove that the only CROSSes that admit a (not necessarily homogeneous) almost quaternionic structure are $H P^{n}$ and $C P^{2}$ .

math.AT2026

On formality of diagrams of Eilenberg-MacLane spaces

Grigory Solomadin, Antoine Touzé

In this paper, we establish formality (over $Q$ ) for diagrams of Eilenberg-MacLane spaces of any height $n \geq 1$ . This implies spectral sequence (over $Q$ ) colla…

math.AT2026

Equivariant cohomology epimorphisms and face ring quotients for Hamiltonian and complexity one GKM $_{4}$ manifolds

Oliver Goertsches, Grigory Solomadin

Given a GKM $_{3}$ action of a torus $K$ on a manifold $M$ with GKM graph $Γ$ , we show that for any extension of $Γ$ to an abstract GKM graph the corresponding restriction map in equi…

math.GT2026

Independence of homogeneous GKM manifolds and symmetric spaces

Shintaro Kuroki, Grigory Solomadin

Let $G / H$ be a simply connected homogeneous space of maximal rank. Then the maximal torus $T$ -action on $G / H$ is a GKM manifold. We call the $T$ -action $j$ -independent if any $i(\l…

math.AT2025

Operads of moduli spaces of points in $C^{d}$ revisited

Vladimir Dotsenko, Eduardo Hoefel, Sergey Shadrin +1

We study the operad structure on the homology of moduli spaces of pointed rooted trees of $d$ -dimensional projective spaces, introduced by Chen, Gibney and Krashen a couple of deca…

math.AT2025

Extensions of realizable Hamiltonian and complexity one GKM $_{4}$ graphs

Oliver Goertsches, Grigory Solomadin

We prove that the GKM graphs of GKM $_{4}$ manifolds that are either Hamiltonian or of complexity one extend to torus graphs. The arguments are based on a reformulation of the extensi…

math.AT2025

Sheaf theory: from deep geometry to deep learning

Anton Ayzenberg, Thomas Gebhart, German Magai +1

This paper provides an overview of the applications of sheaf theory in deep learning, data science, and computer science in general. The primary text of this work serves as a frien…

math.AT2024

Rational cohomology of toric diagrams

Grigory Solomadin

In this note, (rational) Betti numbers of homotopy colimits for toric diagrams and their classifying spaces are described in terms of sheaf cohomology over CW posets. We prove for…

math.AT2022

Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph

Shintaro Kuroki, Grigory Solomadin

In this paper, we introduce the GKM theoretical counterpart of the equivariant complex vector bundles as the "leg bundle". We also provide a definition for the projectivization of…

math.CO2022★ 1 cited

On independent GKM-graphs without nontrivial extensions

Grigory Solomadin

In this paper an example of a $k$ -independent $(n, k)$ -type GKM-graph without nontrivial extensions is constructed for any $n \geq k \geq 3$ . It is shown that this example cannot be r…

math.AT2022★ 3 cited

How is a graph not like a manifold?

Anton Ayzenberg, Mikiya Masuda, Grigory Solomadin

For an equivariantly formal action of a compact torus $T$ on a smooth manifold $X$ with isolated fixed points we investigate the global homological properties of the graded poset $…

math.AT2022★ 1 cited

On the homotopy decomposition for the quotient of a moment-angle complex and its applications

Ivan Limonchenko, Grigory Solomadin

In this paper we prove that the quotient of any real or complex moment-angle complex by any closed subgroup in the naturally acting compact torus on it is equivariantly homotopy eq…

math.AT2019

Cohomology rings and algebraic torus actions on hypersurfaces in the product of projective spaces and bounded flag varieties

Grigory Solomadin

In this paper, for any Milnor hypersurface we find the largest dimension of effective algebraic torus actions on it. The proof of the corresponding theorem is based on the computat…

math.AT2018

The explicit geometric constructions of bordism of Milnor hypersurface $H_{1, n}$ and $C P^{1} \times C P^{n - 1}$

Grigory Solomadin

In the present paper we construct two new explicit complex bordisms between any two projective bundles over $C P^{1}$ of the same complex dimension, including the Milnor hyp…

math.KT2018

Quasitoric stably normally split manifolds

Grigory Solomadin

A smooth stably complex manifold is called a totally tangentially/normally split manifold (TTS/TNS-manifold, for short, resp.) if the respective complex tangential/normal vector bu…

math.AT2017

Quasitoric totally normally split representatives in unitary cobordism ring

Grigory Solomadin

The present paper generalises the results of Ray and Buchstaber-Ray, Buchstaber-Panov-Ray in unitary cobordism theory. I prove that any class $x \in Ω_{U}^{*}$ of the unitary cobord…

math.AT2016★ 1 cited

Projective toric generators in the unitary cobordism ring

Yury Ustinovskiy, Grigory Solomadin

By the classical result of Milnor and Novikov, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: $Ω^U_*\simeq \mathbb Z[a_1,a_2,\…

Cellular approximations for nonsymmetric homotopy operads

Brieskorn spheres bound orbit spaces of torus manifolds

Almost quaternionic structures on compact rank one symmetric spaces

On formality of diagrams of Eilenberg-MacLane spaces

Equivariant cohomology epimorphisms and face ring quotients for Hamiltonian and complexity one GKM4​ manifolds

Independence of homogeneous GKM manifolds and symmetric spaces

Operads of moduli spaces of points in Cd revisited

Extensions of realizable Hamiltonian and complexity one GKM4​ graphs

Sheaf theory: from deep geometry to deep learning

Rational cohomology of toric diagrams

Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph

On independent GKM-graphs without nontrivial extensions

How is a graph not like a manifold?

On the homotopy decomposition for the quotient of a moment-angle complex and its applications

Cohomology rings and algebraic torus actions on hypersurfaces in the product of projective spaces and bounded flag varieties

The explicit geometric constructions of bordism of Milnor hypersurface H1,n​ and CP1×CPn−1

Quasitoric stably normally split manifolds

Quasitoric totally normally split representatives in unitary cobordism ring

Projective toric generators in the unitary cobordism ring

Equivariant cohomology epimorphisms and face ring quotients for Hamiltonian and complexity one GKM $_{4}$ manifolds

Operads of moduli spaces of points in $C^{d}$ revisited

Extensions of realizable Hamiltonian and complexity one GKM $_{4}$ graphs

The explicit geometric constructions of bordism of Milnor hypersurface $H_{1, n}$ and $C P^{1} \times C P^{n - 1}$