Tseleung So

activity

20162026

most citedThe homotopy classification of four-dimensional toric orbifolds

3 citations · 9 across the 15 of their papers we have counts for

collaborators

19 papers

math.AT2026

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…

math.AT2026

On the homotopy types of $4$ -dimensional toric orbifolds

Tyrone Cutler, Tseleung So

The cohomological rigidity problem for toric orbifolds asks when an integral cohomology isomorphism implies a homotopy equivalence. In this paper we reformulate the cohomological r…

math.AT2026

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…

math.RA2025

Realizing orders in rational sphere product algebras with three generators

Tseleung So, Donald Stanley, Stephen Theriault +1

The realization problem asks which algebras can be realized as the cohomology of spaces. We study this problem in the context of the orders in a graded rational exterior algebra on…

math.AT2025

Steenrod operations for $4$ -dimensional toric orbifolds

Tseleung So

We prove necessary and sufficient conditions for the existence of non-trivial Steenrod actions on the mod- $2$ cohomology of 4-dimensional toric orbifolds. As applications, the stab…

math.AT2024

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…

math.AT2024

Homotopy rigidity for quasitoric manifolds over a product of $d$ -simplices

Xin Fu, Tseleung So, Jongbaek Song +1

For a fixed integer $d \geq 1$ , we show that two quasitoric manifolds over a product of $d$ -simplices are homotopy equivalent after appropriate localization, provided that their int…

math.AT2023

Suspension splittings of 5-dimensional Poincaré duality complexes and their applications

Steven Amelotte, Tyrone Cutler, Tseleung So

Let $X$ be a connected, orientable, 5-dimensional Poincaré duality complex with torsion-free $H_{1} (X; Z)$ . We show that $Σ X$ is homotopy equivalent to a wedge of recognisabl…

math.AT2023

Weighted polyhedral products and Steenrod's problem

Tseleung So, Donald Stanley, Stephen Theriault

We construct a weighted version of polyhedral products and compute its cohomology in special cases. This is applied to resolve Steenrod's cohomology realization problem in a case r…

math.AT2023

The integral cohomology rings of four-dimensional toric orbifolds

Xin Fu, Tseleung So, Jongbaek Song

Let $X (P, λ)$ be a 4-dimensional toric orbifold associated to a polygon $P$ and a characteristic function $λ$ . Assuming that $X (P, λ)$ is locally smooth over a vertex of $P$ , we dete…

math.AT2021

The homotopy type of a once-suspended 6-manifold and its applications

Tyrone Cutler, Tseleung So

Let $M$ be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of $Σ M$ in terms of spheres, Moore spaces and other rec…

math.AT2020★ 3 cited

The homotopy classification of four-dimensional toric orbifolds

Xin Fu, Tseleung So, Jongbaek Song

Let $X$ be a $4$ -dimensional toric orbifold. If $H^{3} (X)$ has a non-trivial odd primary torsion, then we show that $X$ is homotopy equivalent to the wedge of a Moore space and a CW-…

math.AT2020★ 3 cited

Realization of graded monomial ideal rings modulo torsion

Tseleung So, Donald Stanley

Let $A$ be the quotient of a graded polynomial ring $Z [x_{1}, \dots, x_{m}] \otimes Λ [y_{1}, \dots, y_{n}]$ by an ideal generated by monomials with leading coefficients 1. Then we con…

math.AT2019

The suspension of a 4-manifold and its applications

Tseleung So, Stephen Theriault

Let $M$ be a smooth, orientable, closed, connected $4$ -manifold and suppose that $H_{1} (M; Z)$ is finitely generated and has no $2$ -torsion. We give a homotopy decomposition…

math.AT2018★ 2 cited

The homotopy types of $S p (2)$ -gauge groups over closed, simply-connected four-manifolds

Tseleung So, Stephen Theriault

We determine the number of distinct fibre homotopy types for the gauge groups of principal $S p (2)$ -bundles over a closed, simply-connected four-manifold.

math.AT2018

Homotopy types of $S U (n)$ -gauge groups over non-spin 4-manifolds

Tseleung So

Let $M$ be an orientable, simply-connected, closed, non-spin 4-manifold and let $G_{k} (M)$ be the gauge group of the principal $G$ -bundle over $M$ with second Chern class $…

math.AT2018★ 1 cited

Odd primary homotopy types of the gauge groups of exceptional Lie groups

Sho Hasui, Daisuke Kishimoto, Tseleung So +1

The $p$ -local homotopy types of gauge groups of principal $G$ -bundles over $S^{4}$ are classified when $G$ is a compact connected exceptional Lie group without $p$ -torsion in homolog…

math.AT2017

The odd primary order of the commutator on low rank Lie groups

Tse Leung So

Let $G$ be a simply-connected, compact, simple Lie group of low rank relative to a fixed prime $p$ . After localization at $p$ , there is a space $A$ which "generates" $G$ in a certa…

math.AT2016

Homotopy types of gauge groups over non-simply-connected closed 4-manifolds

Tse Leung So

Let $G$ be a simply-connected simple compact Lie group and let $M$ be an orientable smooth closed 4-manifold. In this paper we calculate the homotopy type of the suspension of $M$ …

Homotopy rigidity for quasitoric manifolds over a product of simplices

On the homotopy types of 4-dimensional toric orbifolds

Integral bases for the second degree cohomology of 4-dimensional toric orbifolds

Realizing orders in rational sphere product algebras with three generators

Steenrod operations for 4-dimensional toric orbifolds

Cohomology bases of toric surfaces

Homotopy rigidity for quasitoric manifolds over a product of d-simplices

Suspension splittings of 5-dimensional Poincaré duality complexes and their applications

Weighted polyhedral products and Steenrod's problem

The integral cohomology rings of four-dimensional toric orbifolds

The homotopy type of a once-suspended 6-manifold and its applications

The homotopy classification of four-dimensional toric orbifolds

Realization of graded monomial ideal rings modulo torsion

The suspension of a 4-manifold and its applications

The homotopy types of Sp(2)-gauge groups over closed, simply-connected four-manifolds

Homotopy types of SU(n)-gauge groups over non-spin 4-manifolds

Odd primary homotopy types of the gauge groups of exceptional Lie groups

The odd primary order of the commutator on low rank Lie groups

Homotopy types of gauge groups over non-simply-connected closed 4-manifolds

On the homotopy types of $4$ -dimensional toric orbifolds

Steenrod operations for $4$ -dimensional toric orbifolds

Homotopy rigidity for quasitoric manifolds over a product of $d$ -simplices

The homotopy types of $S p (2)$ -gauge groups over closed, simply-connected four-manifolds

Homotopy types of $S U (n)$ -gauge groups over non-spin 4-manifolds