Haoyang Liu

collaborators

4 papers

math.AG2026

Torus-enriched Motivic Bruhat Complexes and Maximal Compact Groups

Haoyang Liu, Tianle Liu

Bruhat decompositions give cellular models for split algebraic groups, flag varieties, and maximal compact groups, but motivic boundaries retain orientation and torus-translation d…

math.AG2026

Cellular $A^{1}$ -homology of wonderful models of subspace arrangements

Haoyang Liu, Keyao Peng

We compute the cellular $A^{1}$ -homology of De Concini--Procesi wonderful models of subspace arrangements. For a building set $G$ over a field $k$ , we identify the…

math.AG2026

Cellular $A^{1}$ -Homology from Bruhat Boundary Matrices of Split Semisimple Flag Varieties

Haoyang Liu, Tianle Liu

Let $k$ be a perfect field of characteristic different from 2, we compute the cellular $A^{1}$ -homology of the flag varieties $G / P_{I^} $ attached to split semisimple simply co…

math.AG2025

Cellular $A^{1}$ -Homology of Smooth Toric Varieties

Haoyang Liu, Keyao Peng

In this paper, we present the calculations of cellular $A^{1}$ -homology for smooth toric varieties, along with an explicit description of pure shellable cases. Consequently,…

Torus-enriched Motivic Bruhat Complexes and Maximal Compact Groups

Cellular A1-homology of wonderful models of subspace arrangements

Cellular A1-Homology from Bruhat Boundary Matrices of Split Semisimple Flag Varieties

Cellular A1-Homology of Smooth Toric Varieties

Cellular $A^{1}$ -homology of wonderful models of subspace arrangements

Cellular $A^{1}$ -Homology from Bruhat Boundary Matrices of Split Semisimple Flag Varieties

Cellular $A^{1}$ -Homology of Smooth Toric Varieties