7 papers
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…
Notions of simple type for Bauer--Furuta invariants
Tsuyoshi Kato, Daisuke Kishimoto, Nobuhiro Nakamura +1
By extending the notion of simple type for the Seiberg--Witten invariant of a 4-manifold, we introduce notions of BF blowup simple type and BF homogeneous type for the Bauer--Furut…
Uniform Lefschetz fixed-point theory
Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya
We develop a Lefschetz fixed-point theory for uniformly continuous self-maps of noncompact manifolds of bounded geometry. For a uniform, simply-connected, complete Riemannian manif…
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…
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…
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…
Homotopy commutativity in symmetric spaces
Daisuke Kishimoto, Yuki Minowa, Toshiyuki Miyauchi +1
We extend the former results of Ganea and the two of the authors with Takeda on the homotopy commutativity of the loop spaces of Hermitian symmetric spaces such that the loop space…