3 papers
math.AT2026
Discrete homotopy groups of cubical sets
Daisuke Kishimoto, Yichen Tong
We extend the notion of discrete homotopy groups of graphs to arbitrary cubical sets, and show that the discrete homotopy groups of quasisymmetric cubical sets are naturally isomor…
math.AT2025
The fundamental group and the magnitude-path spectral sequence of a directed graph
Daisuke Kishimoto, Yichen Tong
The fundamental group of a directed graph admits a natural sequence of quotient groups called -fundamental groups, and the -fundamental groups can capture properties of a dir…
math.AT2025
Homotopy commutativity in quasitoric manifolds
Sho Hasui, Daisuke Kishimoto, Yichen Tong +1
We prove that the loop space of a quasitoric manifold is homotopy commutative if and only if the underlying polytope is a product of -simplices and the characteristic…