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math.GT2024
Morse inequalities for noncompact manifolds
Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya
We establish Morse inequalities for a noncompact manifold with a cocompact and properly discontinuous action of a discrete group, where Morse functions are not necessarily invarian…
math.AT2024
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.AT2024
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…