[Japanese]
Center for Integrated Sciences and Humanities
Fukushima Medical University
１Hikariga-oka, Fukushima City 960-1295, JAPAN
Research interests
Gauge theory and 4-dimensional topology -->
Research Gate
Publications and preprints
- Upper bounds for virtual dimensions of Seiberg-Witten moduli spaces (with T. Kato, D. Kishimoto and K. Yasui), preprint, [arXiv]
- The simple type conjecture for mod 2 Seiberg-Witten invariants (with T. Kato and K. Yasui), J. Eur. Math. Soc. (2022), [JEMS], [arXiv]
- A note on exotic families of 4-manifolds (with T. Kato and H. Konno), Proc. Amer. Math. Soc. 151 (2023), 2695-2705, [Proc AMS] [arXiv]
- Constraints on families of smooth 4-manifolds from $\mathrm{Pin}^-(2)$-monopole (with H. Konno), Algebraic & Geometric Topology 23 (2023) 419-438, [AGT], [arXiv]
- Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds (with T. Kato and H. Konno), Compositio Mathematica , Volume 157 , Issue 4 , April 2021 , pp. 770 - 808, [arXiv]
- Real structures and the $\mathrm{Pin}^-(2)$-monopole equations, Internat. J. Math. Volume 31, Issue 14 (2020), [Int J Math], [arXiv].
- Yamabe Invariants and the $\mathrm{Pin}^-(2)$-monopole Equations (with M.Ishida and S. Matsuo), Math. Res. Lett. 23 (2016) Number 4, 1049 -1069, [MRL], [arXiv].
- $\mathrm{Pin}^-(2)$-monopole invariants, J. Differential Geom. 101, Number 3 (2015), 507-549, [JDG], [arXiv].
- $\mathrm{Pin}^-(2)$-monopole equations and intersection forms with local coefficients of 4-manifolds, Math. Ann. 357 (2013), pp 915-939, [Math.Ann.], [arXiv]
- Mod $p$ equality theorem for Seiberg-Witten invariants under $\mathbb{Z}_p$-actions, Tokyo J. of Math. 37 No. 1 (2014), 21-29. [Tokyo J. of Math], [arXiv].
- Smoothability of $\mathbb{Z} \times \mathbb{Z}$-actions on 4-manifolds, Proc. Amer. Math. Soc. 138 (2010), 2973-2978. [PAMS], [arXiv].
- Bauer-Furuta invariants under $\mathbb{Z}_2$-actions, Math. Z. 262, (2009), 219-233, [Math.Z.], [arXiv].
- Nonsmoothable group actions on elliptic surfaces (with X. Liu), Topology Appl. 155 (2008), 946--964, [Science Direct], [arXiv].
- Pseudofree $\mathbb{Z}/3$-actions on $K3$ surfaces (Joint with Ximin Liu),
Proc. Amer. Math. Soc. 135 (2007), no. 3, 903--910, [PAMS], [arXiv].
- Mod $p$ vanishing theorem of Seiberg-Witten invariants for 4-manifolds with $\mathbb{Z}_p$-actions, Asian J. Math. 10 (2006), no. 4, 731--748, [AJM], [arXiv].
- The Seiberg-Witten equations for families and diffeomorphisms of $4$-manifolds, Asian J. Math. Vol. 7, No. 1, pp. 133-138 (2003), [AJM], Correction: Asian Journal of Mathematics, Vol.9, No.1 (2005), pp 185-186, [AJM].
- A free $\mathbb{Z}_p$-action and the Seiberg-Witten invariants, J. Korean Math. Soc. Vol.39 No.1, pp.103-117,(2002), [JKMS]
Book
- T.Kato and N. Nakamura: Monopole Maps and $L^2$-cohomology [Springer]
Talks
- Upper bounds for virtual dimensions of Seiberg-Witten moduli spaces [PDF], Gauge Theory in Kyoto, (Kyoto University，2023.3.24)
- Families Seiberg-Witten invariants and topology of spin families of 4-manifolds [PDF], 4-dimensional Topology and Gauge Theory, (Escale Yokohama，2020.1.29)
- Real structures and the Pin^-(2)-monopole equations [PDF], Gauge Theory in Fukuoka (Yanagawa, 2018.2.19)
- Recent development of Seiberg-Witten Floer theory [PDF], Invariants of 3-manifolds related to the Casson invariant (RIMS, Kyoto univ., 2017.1.26)
- Pin(2)-monopole theory
- Intersection forms with local coefficients [PDF], GAGT2016 (Tokyo University of Science, 2016.12.12)
- Pin(2)-monopole invariants [PDF], GAGT2016 (Tokyo Institute of Technology, 2016.12.14)
- Yamabe invariants and Pin(2)-monopole equations [Abstract(Japanese)], [PDF], The 63th Geometry Symposium (Okayama University, 2016.8.29)
- Pin(2)-monopole equations and Yamabe invariants [PDF], Four dimensional topology(Osaka City University, Nov 22, 2014)
- Pin(2)-monopole equations and applications [PDF], 2013 SNU/KIAS Toplogy Winter School
- Pin(2)-monopole invariants and its applications [PDF], Hiroshima Topology Conference "Four Dimensional Topology"(Hiroshima University, 2012.11.14-16)
- Pin^-(2)-monopole equations and intersection forms with local coefficients of 4-manifolds [PDF], Topology tuesday seminar (University of Tokyo, 2010.11.30)
- Smoothability of Z x Z-actions on 4-manifolds [PDF], Hiroshima Topology Conference Four Dimensional Topology(2010.1.18-20)
- Nonsmoothable involutions on K3 and K3#K3 [PDF], Hiroshima Topology Conference Four Dimensional Topology(2009.1.26-28)
- Low and infinite dimensional geometry (2007.9.11-14)
- Manolescu's Seiberg-Witten Floer homotopy types, [PDF]
- The Seiberg-Witten equations for families and diffeomorphisms of 4-manifolds, [PDF]
- Bauer-Furuta invariants and a non-smoothable involution on K3#K3 (2007.8.8), The 54th Topology symposium,
nnaka[at]fmu.ac.jp ([at]->@)
Fukushima Medical University