Hisaaki Endo

Research

My research interests are mainly in topology of 4-manifolds and mapping class groups of surfaces, especially in various aspects 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).

Surveys (refereed)

• 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.

Preprints

• 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.

Current Students

15 students belong to our laboratory in AY 2022-2023: 2 postdocs, 7 in doctor course, 5 in master course, and 1 undergraduate.

JSPS Postdoctoral Fellow (PD)

• Nobuo Iida (gauge theory, Seiberg-Witten theory, contact geometry, symplectic geometry)

Doctor Course

• Ayaka Ise (homotopy 4-spheres, 2-knots)
• Koji Yamazaki (contact structure, Engel structure, h-principle)
• Kazunori Iwaki (homotopy 4-spheres, number theory)
• Hokuto Tanimoto (4-manifolds, trisection)
• Tatsumasa Suzuki (4-manifolds, Brieskorn spheres, trisection, knot surgery, outer surgery)
• Tsukasa Isoshima (4-manifolds, trisection)
• Chihaya Jibiki (left-orderings, dynamics, 3-manifolds)

Master Course

• Kenji Takahashi (4-manifold)
• Minami Taniguchi (bridge trisection of knotted surfaces, Kirby-Thompson invariant for bridge trisection, bridge trisection of immersed surfaces)

Former Members

• Wataru Yuasa (Osaka Central Advanced Mathematical Institute)
• Takuya Ukida (National Institute of Technology, Anan College)
• Takahiro Oba (Osaka University)
• Genki Omori (Tokyo University of Science)
• Erika Kuno (Osaka University)
• Takahiro Matsuyuki (Linea Co.,Ltd., Keio University)

Professional Information

Date of birth: December 22, 1968; Place of birth: Fukushima Prefecture

Academic Employment

April 2012-Present: Professor, Department of Mathematics, Tokyo Institute of Technology
April 2003-March 2012: Associate Professor, Department of Mathematics, Osaka University
April 2000-March 2003: Assistant Professor, Department of Mathematics, Tokyo Institute of Technology
November 1999-March 2000: Visiting Researcher, Mathematics Institute, University of Munich
January 1996-December 1998: JSPS Research Fellowships for Young Scientists (DC2/PD)

Education

December 1997: Doctor of Science, Osaka University
March 1993: Master of Science, Osaka University
March 1991: Bachelor of Science, Osaka University

Contact Information

Address: Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
Mailbox: H-9
Office: Room 204, Main Building, Tokyo Institute of Technology
email: endo "attomaaku" math.titech.ac.jp