27 citations · 67 across the 19 of their papers we have counts for
20 papers
Homotopy rigidity for quasitoric manifolds over a product of simplices
Xin Fu, Tseleung So, Jongbaek Song +1
We consider a variation of the Cohomological Rigidity Problem: whether two quasitoric manifolds whose cohomology rings are isomorphic are homotopy equivalent. We show that if two q…
Integral bases for the second degree cohomology of 4-dimensional toric orbifolds
Tseleung So, Jongbaek Song
We study toric orbifolds of real dimension four with vanishing odd-degree cohomology and obtain a basis for its degree-two equivariant cohomology with integral coefficients by iden…
Cohomology bases of toric surfaces
Xin Fu, Tseleung So, Jongbaek Song
Given a compact toric surface, the multiplication of its rational cohomology can be described in terms of the intersection products of Weil divisors, or in terms of the cup product…
Homotopy rigidity for quasitoric manifolds over a product of -simplices
Xin Fu, Tseleung So, Jongbaek Song +1
For a fixed integer , we show that two quasitoric manifolds over a product of -simplices are homotopy equivalent after appropriate localization, provided that their int…
The integral cohomology rings of four-dimensional toric orbifolds
Xin Fu, Tseleung So, Jongbaek Song
Let be a 4-dimensional toric orbifold associated to a polygon and a characteristic function . Assuming that is locally smooth over a vertex of , we dete…
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…
Toric surfaces with symmetries by reflections
Jongbaek Song
Let be a reflection group in a plane and a rational polygon that is invariant under the -action. The action of on induces a -action on the toric variety …
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}^…
Conic decomposition of a toric variety and its application to cohomology
Seonjeong Park, Jongbaek Song
We introduce the notion of a \emph{conic sequence} of a convex polytope. It is a way of building up a polytope starting from a vertex and attaching faces one by one with certain re…
Toric orbifolds associated with partitioned weight polytopes in classical types
Tatsuya Horiguchi, Mikiya Masuda, John Shareshian +1
Given a root system of type , , , or in Euclidean space , let be the associated Weyl group. For a point not orthogonal to any of the roots…
The homotopy classification of four-dimensional toric orbifolds
Xin Fu, Tseleung So, Jongbaek Song
Let be a -dimensional toric orbifold. If has a non-trivial odd primary torsion, then we show that is homotopy equivalent to the wedge of a Moore space and a CW-…
Poincare polynomials of generic torus orbit closures in Schubert varieties
Eunjeong Lee, Mikiya Masuda, Seonjeong Park +1
The closure of a generic torus orbit in the flag variety of type is known to be a permutohedral variety and its Poincare polynomial agrees with the Eulerian polynomial. I…
Equivariant cohomological rigidity of certain -manifolds
Soumen Sarkar, Jongbaek Song
We introduce the category of {\it locally -standard -manifolds} which includes well-known classes of manifolds such as toric and quasitoric manifolds, good contact toric mani…
GKM theory for orbifold stratified spaces and application to singular toric varieties
Soumen Sarkar, Jongbaek Song
We study the GKM theory for a equivariant stratified space having orbifold structures in tis successive quotients. Then, we introduce the notion of an \emph{almost simple polytope}…
Torus orbifolds with two fixed points
Alastair Darby, Shintaro Kuroki, Jongbaek Song
The main objects of this paper are torus orbifolds that have exactly two fixed points. We study the equivariant topological type of these orbifolds and consider when we can use the…
Equivariant cohomology of torus orbifolds
Alastair Darby, Shintaro Kuroki, Jongbaek Song
We calculate the integral equivariant cohomology, in terms of generators and relations, of locally standard torus orbifolds whose odd degree ordinary cohomology vanishes. We begin…
Infinite Families of Equivariantly Formal Toric Orbifolds
Anthony Bahri, Soumen Sarkar, Jongbaek Song
The simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric…
On integral cohomology of certain orbifolds
Anthony Bahri, Dietrich Notbohm, Soumen Sarkar +1
The CW structure of certain spaces, such as effective orbifolds, can be too complicated for computational purposes. In this paper we use the concept of -CW complex stru…
Flag Bott manifolds and the toric closure of a generic orbit associated to a generalized Bott manifold
Shintarô Kuroki, Eunjeong Lee, Jongbaek Song +1
To a direct sum of holomorphic line bundles, we can associate two fibrations, whose fibers are, respectively, the corresponding full flag manifold and the corresponding projective…
On the Integral Cohomology Ring of Toric Orbifolds and Singular Toric Varieties
Anthony Bahri, Soumen Sarkar, Jongbaek Song
We examine the integral cohomology rings of certain families of -dimensional orbifolds that are equipped with a well-behaved action of the -dimensional real torus. These…