12 papers
Seiberg-Witten theory on finite covering spaces of spin 4-manifolds
Tsuyoshi Kato, Doman Takata
We compute the equivariant Bauer-Furuta degree, when a finite group acts freely on a spin 4-manifold. In the case when the group is cyclic of order power of two, Bryan gave a formu…
Hilbert bundles with ends
Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya
Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and…
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…
Adaptive Signal Variances: CNN Initialization Through Modern Architectures
Takahiko Henmi, Esmeraldo Ronnie Rey Zara, Yoshihiro Hirohashi +1
Deep convolutional neural networks (CNN) have achieved the unwavering confidence in its performance on image processing tasks. The CNN architecture constitutes a variety of differe…
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…