61 citations · 431 across the 48 of their papers we have counts for
38 papers · 1 filter
A stability theorem for bigraded persistence barcodes
Anthony Bahri, Ivan Limonchenko, Taras Panov +2
We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated…
Equivariant cohomology of moment-angle complexes with respect to coordinate subtori
Taras Panov, Indira Zeinikesheva
We compute the equivariant cohomology of moment-angle complexes with respect to the action of coordinate subtori . We give…
Minimally non-Golod face rings and Massey products
Ivan Limonchenko, Taras Panov
We give a correct statement and a complete proof of the criterion obtained by Grbić, Panov, Theriault and Wu for the face ring of a simplicial complex to be Golod ov…
Double cohomology of moment-angle complexes
Ivan Limonchenko, Taras Panov, Jongbaek Song +1
We put a cochain complex structure on the cohomology of a moment-angle complex and call the resulting cohomology the double cohomology, ${HH}^…
-linear operations in complex cobordism and the -spherical bordism theory
Georgy Chernykh, Taras Panov
We study the -linear operations in complex cobordism and prove that they are generated by the well-known geometric operations . For the theory of -spherica…
One-relator groups and algebras related to polyhedral products
Jelena Grbić, Marina Ilyasova, Taras Panov +1
We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex , we specify a necessary and sufficient c…
SU-bordism: structure results and geometric representatives
Georgy Chernykh, Ivan Limonchenko, Taras Panov
In the first part of this survey we give a modernised exposition of the structure of the special unitary bordism ring, by combining the classical geometric methods of Conner-Floyd,…
Higher Whitehead products in moment-angle complexes and substitution of simplicial complexes
Semyon Abramyan, Taras Panov
We study the question of realisability of iterated higher Whitehead products with a given form of nested brackets by simplicial complexes, using the notion of the moment-angle comp…
Calabi-Yau hypersurfaces and SU-bordism
Ivan Limonchenko, Zhi Lu, Taras Panov
Batyrev constructed a family of Calabi-Yau hypersurfaces dual to the first Chern class in toric Fano varieties. Using this construction, we introduce a family of Calabi-Yau manifol…
The homotopy theory of polyhedral products associated with flag complexes
Taras Panov, Stephen Theriault
If is a simplicial complex on vertices the flagification of is the minimal flag complex on the same vertex set that contains . Letting be the set of vertic…
On manifolds defined by 4-colourings of simple 3-polytopes
Victor Buchstaber, Taras Panov
Let be the class of combinatorial 3-dimensional simple polytopes , different from a tetrahedron, without 3- and 4-belts of facets. By the results of Pogorelov and…
Cohomological rigidity of manifolds defined by right-angled 3-dimensional polytopes
Victor Buchstaber, Nikolay Erokhovets, Mikiya Masuda +2
A family of closed manifolds is called cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. We establish cohomologic…
On the cohomology of quotients of moment-angle complexes
Taras Panov
We describe the cohomology of the quotient Z_K/H of a moment-angle complex Z_K by a freely acting subtorus H in T^m by establishing a ring isomorphism of H*(Z_K/H,R) with an approp…
On toric generators in the unitary and special unitary bordism rings
Zhi Lu, Taras Panov
We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a triv…
Geometric structures on moment-angle manifolds
Taras Panov
The moment-angle complex Z_K is cell complex with a torus action constructed from a finite simplicial complex K. When this construction is applied to a triangulated sphere K or, in…
Homotopy types of moment-angle complexes for flag complexes
Jelena Grbic, Taras Panov, Stephen Theriault +1
We study the homotopy types of moment-angle complexes, or equivalently, of complements of coordinate subspace arrangements. The overall aim is to identify the simplicial complexes…
Toric Topology
Victor Buchstaber, Taras Panov
Toric topology emerged in the end of the 1990s on the borders of equivariant topology, algebraic and symplectic geometry, combinatorics and commutative algebra. It has quickly grow…
Toric Topology. Chapter 2: Combinatorial structures
Victor Buchstaber, Taras Panov
This is the second chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
Moment-angle manifolds and complexes. Lecture notes KAIST'2010
Taras Panov
These are notes of the lectures given during the Toric Topology Workshop at the Korea Advanced Institute of Science and Technology in February 2010. We describe several approaches…
Moment-angle complexes from simplicial posets
Zhi Lu, Taras Panov
We extend the construction of moment-angle complexes to simplicial posets by associating a certain T^m-space Z_S to an arbitrary simplicial poset S on m vertices. Face rings Z[S] o…
Toric Genera
Victor M. Buchstaber, Taras E. Panov, Nigel Ray
Our primary aim is to develop a theory of equivariant genera for stably complex manifolds equipped with compatible actions of a torus T^k. In the case of omnioriented quasitoric ma…
Toric cohomological rigidity of simple convex polytopes
Suyoung Choi, Taras Panov, Dong Youp Suh
A simple convex polytope is \emph{cohomologically rigid} if its combinatorial structure is determined by the cohomology ring of a quasitoric manifold over . Not every ha…
Categorical aspects of toric topology
Taras Panov, Nigel Ray
We argue for the addition of category theory to the toolkit of toric topology, by surveying recent examples and applications. Our case is made in terms of toric spaces X_K, such as…
Spaces of polytopes and cobordism of quasitoric manifolds
Victor M. Buchstaber, Taras E. Panov, Nigel Ray
Our aim is to bring the theory of analogous polytopes to bear on the study of quasitoric manifolds, in the context of stably complex manifolds with compatible torus action. By way…