Hyeontae Jang

Toric wedge induction and toric lifting property for piecewise linear spheres with few vertices

Suyoung Choi, Hyeontae Jang, Mathieu Vallée

Abstract Let be an ‐dimensional piecewise linear sphere on , where . There are a canonical action of ‐dimensional torus on the moment‐angle complex , and a canonical action of on the real moment‐angle complex , where is the additive group with …

kr, fr (code pays fourni par la source)

Strong cohomological rigidity of Bott manifolds

Suyoung Choi, Taekgyu Hwang, Hyeontae Jang

We show that two Bott manifolds are diffeomorphic if and only if their integral cohomology rings are isomorphic as graded rings. In fact, we prove that any graded cohomology ring isomorphism between two Bott manifolds is induced by a diffeomorphism.

kr (code pays fourni par la source)

Complete non-singular toric varieties with Picard number 4

Suyoung Choi, Hyeontae Jang, Mathieu Vallée

We classify all complete non-singular toric varieties with Picard number four via a combinatorial framework based on fanlike simplicial spheres and characteristic maps. This classification yields $59$ fanlike seeds with Picard number four, along with all toric manifolds supported by them. As …

kr, be (code pays fourni par la source)

The characterization of (𝑛 − 1)-spheres with 𝑛 + 4 vertices having maximal Buchstaber number

Suyoung Choi, Hyeontae Jang, Mathieu Vallée

Abstract We present a computationally efficient algorithm that is suitable for graphic processing unit implementation. This algorithm enables the identification of all weak pseudo-manifolds that meet specific facet conditions, drawn from a given input set. We employ this approach to enumerate toric …

kr, fr (code pays fourni par la source)

Toric wedge induction and toric lifting property for piecewise linear spheres with a few vertices

Suyoung Choi, Hyeontae Jang, Mathieu Vallée

Let $K$ be an $(n-1)$-dimensional piecewise linear sphere on $[m]$, where $m\leq n+4$. There are a canonical action of $m$-dimensional torus $T^m$ on the moment-angle complex $\mathcal{Z}_K$, and a canonical action of $\mathbb{Z}_2^m$ on the real moment-angle complex $\mathbb{R}\mathcal{Z}_K$, where $\mathbb{Z}_2$ is …

The characterization of (n-1)-spheres with n+4 vertices having maximal Buchstaber number

Suyoung Choi, Hyeontae Jang, Mathieu Vallée

16 pages, 4 tables, 1 figure, 1 algorithm

kr, fr (code pays fourni par la source)

GPU Algorithm for Enumerating PL Spheres of Picard Number 4: Application to Toric Topology

Suyoung Choi, Hyeontae Jang, Mathieu Vallée

The fundamental theorem for toric geometry states a toric manifold is encoded by a complete non-singular fan, whose combinatorial structure is the one of a PL sphere together with the set of generators of its rays. The wedge operation on a PL …

kr, fr (code pays fourni par la source)

Strong Cohomological rigidity of Bott manifolds

Suyoung Choi, Taekgyu Hwang, Hyeontae Jang

We show that the strong cohomological rigidity conjecture for Bott manifolds is true. Namely, any graded cohomology ring isomorphism between two Bott manifolds is induced by a diffeomorphism.