KEIO RESEARCHERS INFORMATION SYSTEM

Papers 【 Display / hide 】

Papers 【 Display / hide 】

• Combinatorial cusp count and clover invariants

  Baader S., Ishikawa M.

  Mathematical Proceedings of the Cambridge Philosophical Society 180 ( 2 ) 237 - 245 2026.03

  ISSN  03050041

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  We construct efficient topological cobordisms between torus links and large connected sums of trefoil knots. As an application, we show that the signature invariant σ<inf>ω</inf> at ω = ζ<inf>6 </inf>takes essentially minimal values on torus links among all concordance homomorphisms with the same normalisation on the trefoil knot.

  • Access to Document (DOI)

• Distinguishing 2-knots admitting circle actions by fundamental groups

  Fukuda M., Ishikawa M.

  Revista Matematica Complutense 38 ( 2 ) 307 - 317 2025.05

  ISSN  11391138

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  A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin. A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair of coprime integers uniquely. In this paper, we study, for each pair of coprime integers, if two different 1-knots yield the same branched twist spin, and prove that such a pair of 1-knots does not exist in most cases. Fundamental groups of 3-orbifolds of cyclic type are obtained as quotient groups of the fundamental groups of the complements of branched twist spins. We use these groups for distinguishing branched twist spins.

  • Access to Document (DOI)

• Relative homotopy groups and Serre fibrations for polynomial maps

  Ishikawa M., Nguyen T.T.

  Journal of the Mathematical Society of Japan 77 ( 2 ) 483 - 497 2025.04

  ISSN  00255645

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  Let f be a polynomial map from R^m to Rⁿ with m > n > 0 and t0 be a regular value of f. For a small open ball Dt<inf>0</inf> centered at t0, we show that the map f : f⁻¹(Dt<inf>0</inf>) → Dt<inf>0</inf> is a Serre fibration if and only if f is a Serre fibration over a finite number of certain simple arcs starting at t0. We characterize the fibration f : f⁻¹(Dt<inf>0</inf>) → Dt<inf>0</inf> by relative homotopy groups defined for these arcs and use it to prove the assertion.

  • Access to Document (DOI)

• Non-integral boundary slopes of alternating knots

  Ishikawa M., Mattman T.W., Shimokawa K.

  Geometriae Dedicata 219 ( 1 )  2025.02

  ISSN  00465755

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  We show, for every positive integer n, there is an alternating knot having a boundary slope with denominator n. We make use of Kabaya’s method for boundary slopes and the layered solid torus construction introduced by Jaco and Rubinstein and further developed by Howie et al.

  • Access to Document (DOI)

• Atypical values at infinity of real polynomial maps with 2-dimensional fibers

  Ishikawa M., Nguyen T.T.

  Comptes Rendus Mathematique 363   917 - 932 2025

  ISSN  1631073X

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  We characterize atypical values at infinity of a real polynomial function of three variables by a certain sum of indices of the gradient vector field of the function restricted to a sphere with a sufficiently large radius. This is a three-variable analogue of a result of Coste and de la Puente for real polynomial functions with two variables. We also give a characterization of atypical values at infinity of a real polynomial map whose regular fibers are 2-dimensional surfaces.

  • Access to Document (DOI)

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Papers, etc., Registered in KOARA 【 Display / hide 】

Papers, etc., Registered in KOARA 【 Display / hide 】

• Study of 2-knots that are invariant under circle actions on the 4-sphere

  Ishikawa, Masaharu

  学事振興資金研究成果実績報告書 (慶應義塾大学)  2023

• Study of geometric structures of singularities and manifolds based on polyhedra

  Ishikawa, Masaharu

  科学研究費補助金研究成果報告書 2023

• Research on correspondence between flow-spines and contact structures on 3-manifolds

  Ishikawa, Masaharu

  学事振興資金研究成果実績報告書 (慶應義塾大学)  2020

• Research on correspondence between flow-spines and contact structures on 3-manifolds

  Ishikawa, Masaharu

  学事振興資金研究成果実績報告書 (慶應義塾大学)  2019

• Research on correspondence between flow-spines and contact structures on 3-manifolds

  Ishikawa, Masaharu

  学事振興資金研究成果実績報告書 (慶應義塾大学)  2018

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

Research Projects of Competitive Funds, etc. 【 Display / hide 】

• 低次元多様体からの写像の組み合わせ及び幾何学的視点からの大域的研究

  2023.04

  -

  2026.03

  基盤研究(C), Principal investigator

• 多面体による写像の特異点および多様体の幾何構造の研究

  2019.04

  -

  2022.03

  MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

Courses Taught 【 Display / hide 】

Courses Taught 【 Display / hide 】

• MATHEMATICS FOR ECONOMICS

  2025

• LINEAR ALGEBRA

  2025

• INTRODUCTION TO MATHEMATICS 2

  2025

• INTRODUCTION TO MATHEMATICS 1

  2025

• INTRODUCTION TO MATHEMATICAL ANALYSIS 2

  2025

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