I have been studying Lefschetz fibration as an object that allows both 4-manifold structures and fibration structures. In recent years, I have treated 4-manifolds and fibrations separately and have been investigating them from various perspectives. I hope to eventually integrate the knowledge gained through this process for better understanding of Lefschetz fibrations.
Published Papers (refereed)
H. Endo and A. Pajitnov, On generalized Inoue manifolds, Proceedings of the International Geometry Center 13 (2020), no. 4, 24-39; MR4237776.
K. Akutagawa, H. Endo, and H. Seshadri, A gap theorem for positive Einstein metrics on the four-sphere, Mathematische Annalen 373 (2019), no. 3-4, 1329-1339; MR3953130.
H. Endo and A. Pajitnov, Circle-valued Morse theory for spun knots and surface-links, The Michigan Mathematical Journal 66 (2017), no. 4, 813-830; MR3720325.
H. Endo and A. Pajitnov, On the Morse-Novikov number for 2-knots, Osaka Journal of Mathematics 54 (2017), no. 4, 725-736; MR3715359.
H. Endo and S. Kamada, Counting Dirac braid relators and hyperelliptic Lefschetz fibrations, Transactions of the London Mathematical Society 4 (2017), no. 1, 72-99; MR3653055.
H. Endo, I. Hasegawa, S. Kamada, and K. Tanaka, Charts, signatures, and stabilization of Lefschetz fibrations, In: Interactions between low-dimensional topology and mapping class groups (Max Planck 2013), Geometry and Topology Monographs 19 (2015), 237-267; MR3609910.
H. Endo and S. Kamada, Chart description for hyperelliptic Lefschetz fibrations and their stabilization, Topology and its Applications 196 (2015), Part B, 416-430; MR3430986.
H. Endo, T. E. Mark, and J. Van Horn-Morris, Monodromy substitutions and rational blowdowns, Journal of Topology 4 (2011), no. 1, 227-253; MR2783383.
H. Endo and Y. Z. Gurtas, Lantern relations and rational blowdowns, Proceedings of the American Mathematical Society 138 (2010), no. 3, 1131-1142; MR2566578.
H. Endo, A generalization of Chakiris' fibrations, In: Groups of Diffeomorphisms, Advanced Studies in Pure Mathematics, Vol. 52, pp. 251-282, 2008; MR2509712.
H. Endo and D. Kotschick, Failure of separation by quasi-homomorphisms in mapping class groups, Proceedings of the American Mathematical Society 135 (2007), no. 9, 2747-2750; MR2317948.
H. Endo and S. Nagami, Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations, Transactions of the American Mathematical Society 357 (2005), no. 8, 3179-3199; MR2135741 (2006g:57051).
H. Endo, M. Korkmaz, D. Kotschick, B. Ozbagci, and A. Stipsicz, Commutators, Lefschetz fibrations and the signatures of surface bundles, Topology 41 (2002), no. 5, 961-977; MR1923994 (2003f:57051).
H. Endo and D. Kotschick, Bounded cohomology and non-uniform perfection of mapping class groups, Inventiones mathematicae 144 (2001), no. 1, 169-175; MR1821147 (2001m:57046).
H. Endo, Meyer's signature cocycle and hyperelliptic fibrations, Mathematische Annalen 316 (2000), no. 2, 237-257; MR1741270 (2001b:57047).
H. Endo, A construction of surface bundles over surfaces with non-zero signature, Osaka Journal of Mathematics 35 (1998), no. 4, 915-930; MR1659565 (99m:55017).
H. Endo, Linear independence of topologically slice knots in the smooth cobordism group, Topology and its Applications 63 (1995), no. 3, 257-262; MR1334309 (96c:57010).
H. Endo, Lefschetz fibrations, Sugaku Expositions 34 (2021), no. 2, 175-204; MR4327688.
T. Ashikaga and H. Endo, Various aspects of degenerate families of Riemann surfaces, Sugaku Expositions 19 (2006), no. 2, 171-196; MR2279776.
H. Endo, K. Iwaki, and A. Pajitnov, Cappell-Shaneson polynomials, preprint, arXiv:2507.10885.
H. Endo and A. Pajitnov, On a generalization of Inoue and Oeljeklaus-Toma manifolds, preprint, arXiv:1906.07401.
H. Endo and Y. Z. Gurtas, Positive Dehn twist expression for a Z_3 action on Sigma_g, preprint, arXiv:0808.0752.
Hisaaki Endo and Kenta Hayano, 4-Manifolds and Fibrations - Topology of Lefschetz Fibrations, Kyoritsu Shuppan Co., Ltd., 2024.
Hisaaki Endo, Sets and Topology, Towards Modern Mathematics, Volume 3, Saiensu-Sha Co., Ltd., 2020.