Nobuhiro Nakamura

In dimensione quarta, profunditas.

Gauge Theory / Four-Manifolds / Topology

About me

中村信裕.主な研究テーマはゲージ理論と4次元トポロジー. 4次元多様体の深層構造を探求しています.

📍福島県立医科大学 総合科学教育研究センター 教授

✉️nnaka [at] fmu.ac.jp

Recent Works

Publications

  • B
    Book (2025)

    Monopole Maps and $L^2$-cohomology

    T. Kato and N. Nakamura
    Springer Monographs in Mathematics (SMM)

    View on Springer
  • The simple type conjecture for mod 2 Seiberg-Witten invariants

    T. Kato, N. Nakamura, K. Yasui
    J. Eur. Math. Soc. 25 (2023), no. 12, pp. 4869–4877

    DOI arXiv:2009.06791
  • Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds

    T. Kato, H. Konno, N. Nakamura
    Compositio Mathematica , Volume 157 , Issue 4 , April 2021 , pp. 770 - 808

    DOI arXiv:1906.02943
  • $\mathrm{Pin}^-(2)$ -monopole equations and intersection forms with local coefficients of 4-manifolds

    N. Nakamura
    Math. Ann. 357 (2013), pp 915-939

    DOI arXiv:1009.3624
  • A note on exotic families of 4-manifolds

    T. Kato, H. Konno, N. Nakamura
    Proc. Amer. Math. Soc. 151 (2023), 2695-2705.

    DOI arXiv:2101.00367
  • Constraints on families of smooth $4$-manifolds from $\mathrm{Pin}^-(2)$-monopole

    H. Konno, N. Nakamura
    Algebraic & Geometric Topology 23 (2023) 419-438.

    DOI arXiv:2003.12517
  • Real structures and the $\mathrm{Pin}^−(2)$-monopole equations

    N. Nakamura
    Internat. J. Math. Volume 31, Issue 14 (2020)

    DOI arXiv:1803.11339
  • Yamabe Invariants and the $\mathrm{Pin}^−(2)$-monopole Equations

    M. Ishida, S. Matsuo, N. Nakamura
    Math. Res. Lett. 23 (2016) Number 4, 1049-1069

    DOI arXiv:1505.05948
  • $\mathrm{Pin}^−(2)$-monopole invariants

    N. Nakamura
    J. Differential Geom. 101, Number 3 (2015), 507-549

    DOI arXiv:1303.4870
  • Mod $p$ equality theorem for Seiberg-Witten invariants under $\mathbb{Z}_p$-actions

    N. Nakamura
    J. Tokyo J. of Math. 37 No. 1 (2014), 21-29

    DOI arXiv:0905.3022
  • Smoothability of $\mathbb{Z}\times\mathbb{Z}$-actions on 4-manifolds

    N. Nakamura
    Proc. Amer. Math. Soc. 138 (2010), 2973-2978

    DOI arXiv:0902.3172
  • Bauer-Furuta invariants under $\mathbb{Z}_2$-actions

    N. Nakamura
    Math. Z. 262, (2009), 219-233

    DOI arXiv:0705.1595
  • Nonsmoothable group actions on elliptic surfaces

    X. Liu, N. Nakamura
    Topology Appl. 155 (2008), 946--964

    DOI arXiv:0712.2505
  • Pseudofree $\mathbb{Z}/3$-actions on $K3$ surfaces

    X. Liu, N. Nakamura
    Proc. Amer. Math. Soc. 135 (2007), no. 3, 903--910

    DOI arXiv:0604317
  • Mod $p$ vanishing theorem of Seiberg-Witten invariants for $4$-manifolds with $\mathbb{Z}_p$-actions

    N. Nakamura
    Asian J. Math. 10 (2006), no. 4, 731--748

    DOI arXiv:0602654
  • The Seiberg-Witten equations for families and diffeomorphisms of $4$-manifolds,

    N. Nakamura
    Asian J. Math. Vol. 7, No. 1, pp. 133-138, Correction: Vol.9, No.1 (2005), pp 185-186

    DOI Correction: DOI
  • A free $\mathbb{Z}_p$-action and the Seiberg-Witten invariants

    N. Nakamura
    J. Korean Math. Soc. Vol.39 No.1 (2002), pp.103-117

    DOI

Selected Talks

  • 2023.03.24 / Gauge Theory in Kyoto (Kyoto University)

    Upper bounds for virtual dimensions of Seiberg-Witten moduli spaces

    PDF SLIDE Conference Page
  • 2020.10.29 / Kansai Gauge (On Line)

    Mod 2 Seiberg-Witten simple type

    PDF SLIDE Seminar Page
  • 2020.1.29 / 4-DIMENSIONAL TOPOLOGY AND GAUGE THEORY (Escale Yokohama)

    Families Seiberg-Witten invariants and topology of spin families of 4-manifolds

    PDF SLIDE Conference Page
  • 2018.2.19 / Gauge Theory in Fukuoka (Nishijin/Yanagawa)

    Real structures and the $\mathrm{Pin}^-(2)$-monopole equations

    PDF SLIDE Conference Page
  • 2017.1.26 / Casson不変量に関わる3次元多様体の不変量 (RIMS)

    Recent development of Seiberg-Witten Floer theory

    PDF SLIDE Conference Page
  • 2016.12.12 / GAGT2016

    $\mathrm{Pin}^-(2)$-monopole theory: Intersection forms with local coefficients

    PDF SLIDE Conference Page
  • 2016.12.14 / GAGT2016

    $\mathrm{Pin}^-(2)$-monopole theory: $\mathrm{Pin}^-(2)$-monopole invariants

    PDF SLIDE Conference Page
  • 2016.8.29 / 幾何学シンポジウム (Okayama University)

    山辺不変量と $\mathrm{Pin}^-(2)$ モノポール方程式

    Abstract PDF SLIDE Conference Page
  • 2016.3.12 / 微分トポロジー16 (University of Tsukuba)

    $\mathrm{Pin}(2)$ 同変 Seiberg-Witten Floer $K$ 理論と境界付き $4$ 次元スピン多様体の交叉形式

    Abstract Conference Page
  • 2014.11.22 / 研究集会「4次元トポロジー」 (Osaka Mtropolitan University)

    $\mathrm{Pin}^-(2)$-monopole equations and Yamabe invariants

    PDF SLIDE
  • 2012.12.20 / 2013 SNU/KIAS Toplogy Winter School

    $\mathrm{Pin}^-(2)$-monopole equations and applications

    PDF SLIDE
  • 2012.12.20 / 研究集会「4次元トポロジー」(Hiroshima University)

    $\mathrm{Pin}^-(2)$-monopole invariants and its applications

    PDF SLIDE Conference Page
  • 2011.9.28 / 日本数学会2011年度秋季総合分科会 (Shinshu University)

    $\mathrm{Pin}^-(2)$ モノポール方程式とその応用

    Abstract PDF SLIDE
  • 2010.11.30 / トポロジー火曜セミナー

    $\mathrm{Pin}^-(2)$-monopole equations and intersection forms with local coefficients of 4-manifolds

    PDF SLIDE
  • 2010.1.20 / 研究集会「4次元トポロジー」(Hiroshima University)

    Smoothability of $\mathbb{Z}\times\mathbb{Z}$-actions on $4$-manifolds

    PDF SLIDE
  • 2009.10.19 / キャッソン・フリードマン理論 研究会

    Edmonds-Ewing の理論:Freedman 理論の群作用への応用

    PDF SLIDE Conference Page
  • 2009.1.28 / 研究集会「4次元トポロジー」(Hiroshima University)

    Nonsmoothable involutions on $K3$ and $K3\#K3$

    PDF SLIDE Conference Page
  • 2007.11.22 / 第34回変換群論シンポジウム

    Nonsmoothable group actions in dimension 4

    Abstract PDF SLIDE
  • 2007.9.13 / 研究集会:低次元幾何学と無限次元幾何学 (Tambara)

    Manolescu's Seiberg-Witten Floer homotopy types

    PDF SLIDE Conference Page
  • 2007.9.12 / 研究集会:低次元幾何学と無限次元幾何学 (Tambara)

    The Seiberg-Witten equations for families and diffeomorphisms of $4$-manifolds

    PDF SLIDE Conference Page
  • 2007.8.8 / 第54回トポロジーシンポジウム (Aizu University)

    Bauer-Furuta invariants and a non-smoothable involution on $K3\#K3$

    Abstract PDF SLIDE Conference Page

Network