How is a graph not like a manifold?
A Ayzenberg, M Masuda, G Solomadin - arXiv preprint arXiv:2203.10641, 2022 - arxiv.org
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 …
isolated fixed points we investigate the global homological properties of the graded poset …
Orbit spaces of equivariantly formal torus actions of complexity one
A Ayzenberg, M Masuda - Transformation Groups, 2023 - Springer
Let a compact torus T= T n-1 act on an orientable smooth compact manifold X= X 2 n
effectively, with nonempty finite set of fixed points, and suppose that stabilizers of all points …
effectively, with nonempty finite set of fixed points, and suppose that stabilizers of all points …
The GKM correspondence in dimension 6
O Goertsches, P Konstantis, L Zoller - arXiv preprint arXiv:2210.01856, 2022 - arxiv.org
It follows from the GKM description of equivariant cohomology that the GKM graph of a GKM
manifold has free equivariant graph cohomology, and satisfies a Poincar\'e duality condition …
manifold has free equivariant graph cohomology, and satisfies a Poincar\'e duality condition …
Equivariantly formal 2-torus actions of complexity one
V Gorchakov - arXiv preprint arXiv:2304.00936, 2023 - arxiv.org
In this paper we study a specific class of actions of a $2 $-torus $\mathbb {Z} _2^ k $ on
manifolds, namely, the actions of complexity one in general position. We describe the orbit …
manifolds, namely, the actions of complexity one in general position. We describe the orbit …
Low-dimensional GKM theory
O Goertsches, P Konstantis, L Zoller - arXiv preprint arXiv:2210.06234, 2022 - arxiv.org
GKM theory is a powerful tool in equivariant topology and geometry that can be used to
generalize classical ideas from (quasi) toric manifolds to more general torus actions. After an …
generalize classical ideas from (quasi) toric manifolds to more general torus actions. After an …
Moduli space of weighted pointed stable curves and toric topology of Grassmann manifolds
VM Buchstaber, S Terzić - arXiv preprint arXiv:2410.01059, 2024 - arxiv.org
We relate the theory of moduli spaces $\overline {\mathcal {M}} _ {0,\mathcal {A}} $ of stable
weighted curves of genus $0 $ to the equivariant topology of complex Grassmann manifolds …
weighted curves of genus $0 $ to the equivariant topology of complex Grassmann manifolds …
On independent GKM-graphs without nontrivial extensions
G Solomadin - Boletín de la Sociedad Matemática Mexicana, 2023 - Springer
In this paper, a new obstruction to an extension for GKM-graphs (in sense of Guillemin and
Zara) is given. For aj-independent GKM-graph, we give a comparison result between the …
Zara) is given. For aj-independent GKM-graph, we give a comparison result between the …
Разрешение особенностей пространств орбит
ВМ Бухштабер, С Терзич - Труды Математического института имени …, 2022 - mathnet.ru
1.1. Формулировка и история проблемы. Многие задачи алгебраической топологии,
комплексной, алгебраической и симплектической геометрии, теории действий групп и …
комплексной, алгебраической и симплектической геометрии, теории действий групп и …
A resolution of singularities for the orbit spaces
VM Buchstaber, S Terzic - arXiv preprint arXiv:2009.01580, 2020 - arxiv.org
The problem of the description of the orbit space $ X_ {n}= G_ {n, 2}/T^ n $ for the standard
action of the torus $ T^ n $ on a complex Grassmann manifold $ G_ {n, 2} $ is widely known …
action of the torus $ T^ n $ on a complex Grassmann manifold $ G_ {n, 2} $ is widely known …
Resolution of Singularities of the Orbit Spaces
VM Buchstaber, S Terzić - Proceedings of the Steklov Institute of …, 2022 - Springer
We study the orbit space of the standard action of the compact torus on the complex
Grassmann manifold. We describe the structure of the set of critical points of the generalized …
Grassmann manifold. We describe the structure of the set of critical points of the generalized …