102 citations · 159 across the 33 of their papers we have counts for
6 papers · 1 filter
Vector fields on non-compact manifolds
Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya
Let be a non-compact connected manifold with a cocompact and properly discontinuous action of a discrete group . We establish a Poincaré-Hopf theorem for a bounded vector fi…
Upper bounds for virtual dimensions of Seiberg-Witten moduli spaces
Tsuyoshi Kato, Daisuke Kishimoto, Nobuhiro Nakamura +1
Given a closed four-manifold with and a prime number , we prove that for any mod basic class, the virtual dimension of the Seiberg-Witten moduli space is bounded a…
A note on exotic families of 4-manifolds
Tsuyoshi Kato, Hokuto Konno, Nobuhiro Nakamura
We present a pair of smooth fiber bundles over the circle with a common -dimensional fiber with the following properties: (1) their total spaces are diffeomorphic to each other;…
The simple type conjecture for mod 2 Seiberg-Witten invariants
Tsuyoshi Kato, Nobuhiro Nakamura, Kouichi Yasui
We prove that, under a simple condition on the cohomology ring, every closed 4-manifold has mod 2 Seiberg-Witten simple type. This result shows that there exists a large class of t…
Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds
Tsuyoshi Kato, Hokuto Konno, Nobuhiro Nakamura
We show a rigidity theorem for the Seiberg-Witten invariants mod 2 for families of spin 4-manifolds. A mechanism of this rigidity theorem also gives a family version of 10/8-type i…
ASD moduli spaces over four-manifolds with tree-like ends
Tsuyoshi Kato
In this paper we construct Riemannian metrics and weight functions over Casson handles. We show that the corresponding Atiyah-Hitchin-Singer complexes are Fredholm for some class o…