Organization
School of Science Associate Professor
Title
Associate Professor
Profile
数学者であり、特に位相幾何学(トポロジー)を専門にしている。そのうち３次元多様体のコホモロジーや基本群を中心に研究している。
External link
NOSAKA TAKEFUMI
Research Interests
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Geometry, topology, quandle
Research Areas
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Natural Science / Geometry / low-dimensional topology
Education
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Kyoto University
2009.4 - 2012.3
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Kyoto University
2007.4 - 2009.3
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Kyoto University Faculty of Science
2003.4 - 2007.3
Research History
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Institute of Science Tokyo Associate Professor
2024.10
Country：Japan
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Tokyo Institute of Technology Department of Mathematics Associate Professor
2017.4 - 2024.9
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Kyushu University Faculty of Mathematics assosiated proffesor
2012.10 - 2017.3
Papers
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Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups Reviewed
Takefumi Nosaka
Journal of Knot Theory and Its Ramifications 2026.5
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Symmetric skew-racks and cocycle invariants of closed 3-manifolds Reviewed
Takefumi Nosaka
Algebraic & Geometric Topology 26 ( 4 ) 1451 - 1464 2026.4
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The Dijkgraaf-Witten invariants from second Chern classes Reviewed
Takefumi Nosaka
Math. J. Okayama Univ. 68 63 - 75 2026.1
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Non-acyclic Reidemeister torsions of manifolds of odd dimension Reviewed
Takefumi Nosaka, Naoko Wakijo, Koki Yanagida
Commun. Korean Math. Soc. 40 ( 2 ) 421 - 446 2025.4
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Fox pairings of Poincaré duality groups Reviewed
Takefumi NOSAKA
Hokkaido Mathematical Journal 53 ( 2 ) 2024.6
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A solvable extended logarithm of the Johnson homomorphism Reviewed
Takefumi Nosaka
Journal of Topology and Analysis 17 ( 06 ) 1773 - 1786 2024.2
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Reciprocity of the Chern–Simons invariants of 3-manifolds Reviewed
Takefumi Nosaka
Letters in Mathematical Physics 114 ( 1 ) 2024.1
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Twisted Alexander Invariants of Knot Group Representations Reviewed
Takefumi Nosaka
Tokyo Journal of Mathematics 45 ( 1 ) 2022.6
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Twisted cohomology pairings of knots II; to some Blanchfield pairings
T. Nosaka
Journal of Knot Theory and Its Ramifications 31 ( 07 ) 2022.6
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Cellular chain complexes of universal covers of some 3-manifolds Reviewed
Takefumi Nosaka
J. Math. Sci. Univ. Tokyo 29 ( 1 ) 89 - 113 2022
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Meta-nilpotent quotients of mapping-torus groups and two topological invariants of quadratic forms Reviewed
Takefumi Nosaka
Osaka J. Math 58 ( 2 ) 351 - 365 2021.4
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Twisted Alexander invariants of knot group representations II; computation and duality Reviewed
Takefumi Nosaka
Topology and its Applications 107533 - 107533 2020.12
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Twisted cohomology pairings of knots III; triple cup products Reviewed
Takefumi Nosaka
Hiroshima Mathematical Journal 50 ( 2 ) 2020.7
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Schur multipliers and second quandle homology Reviewed
Rhea Palak Bakshi, Dionne Ibarra, Sujoy Mukherjee, Takefumi Nosaka, Józef H. Przytycki
Journal of Algebra 552 52 - 67 2020.6
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Milnor invariants via unipotent Magnus embeddings Reviewed
Hisatoshi Kodani, Takefumi Nosaka
Topology and its Applications 271 106991 - 106991 2020.2
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Milnor–Orr Invariants from the Kontsevich Invariant Reviewed
Takefumi Nosaka
Publications of the Research Institute for Mathematical Sciences 56 ( 1 ) 173 - 193 2020.1
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On the fundamental relative 3-classes of knot group representations Reviewed
Takefumi Nosaka
Geometriae Dedicata 1 - 24 2019.4
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Cocycles of nilpotent quotients of free groups Reviewed
Takefumi Nosaka
Journal of the Mathematical Society of Japan 2019
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de Rham theory and cocycles of cubical sets from smooth quandles Reviewed
Takefumi Nosaka
Kodai Mathematical Journal 42 ( 1 ) 111 - 129 2019
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Finite presentations of centrally extended mapping class groups Reviewed
Takefumi Nosaka
73 ( 1 ) 103 - 113 2019
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Central extensions of groups and adjoint groups of quandles Reviewed
Takefumi Nosaka
RIMS Kokyuroku Bessatsu B66 167 - 184 2017.6
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Twisted cohomology pairings of knots I; diagrammatic computation Reviewed
Takefumi Nosaka
Geometriae Dedicata 189 ( 1 ) 139 - 160 2017.2
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Bilinear-form invariants of Lefschetz-fibrations over the 2-sphere Reviewed
Takefumi Nosaka
Journal of Gokova Geometry Topology 11 32 - 55 2017
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Longitudes in SL_2 representations of knot groups and Milnor-Witt K_2 groups of fields Reviewed
Takefumi Nosaka
Annals of K-Theory 2 211 - 233 2016.12
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Homotopical interpretation of link invariants from finite quandles Reviewed
Takefumi Nosaka
TOPOLOGY AND ITS APPLICATIONS 193 1 - 30 2015.9
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On third homologies of groups and of quandles via the Dijkgraaf-Witten invariant and Inoue-Kabaya map Reviewed
Takefumi Nosaka
ALGEBRAIC AND GEOMETRIC TOPOLOGY 14 ( 5 ) 2655 - 2691 2014
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Quandle cocycles from invariant theory Reviewed
Takefumi Nosaka
ADVANCES IN MATHEMATICS 245 423 - 438 2013.10
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On quandle homology groups of Alexander quandles of prime order Reviewed
Takefumi Nosaka
Transactions of the American Mathematical Society 365 3413 - 3436 2013.1
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Quandle homotopy invariants of knotted surfaces Reviewed
Takefumi Nosaka
Mathematische Zeitschrift 274 341 - 365 2012.10
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SOME TOPOLOGICAL ASPECTS OF 4-FOLD SYMMETRIC QUANDLE INVARIANTS OF 3-MANIFOLDS Reviewed
Eri Hatakenaka, Takefumi Nosaka
INTERNATIONAL JOURNAL OF MATHEMATICS 23 ( 7 ) 2012.7
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On homotopy groups of quandle spaces and the quandle homotopy invariant of links Reviewed
Takefumi Nosaka
TOPOLOGY AND ITS APPLICATIONS 158 ( 8 ) 996 - 1011 2011.5
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4-fold symmetric quandle invariants of 3-manifolds Reviewed
Takefumi Nosaka
ALGEBRAIC AND GEOMETRIC TOPOLOGY 11 ( 3 ) 1601 - 1648 2011
Books
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Quandles and topological pairs : symmetry, knots, and cohomology
Nosaka, Takefumi（ Role： Sole author）
Springer,[Amazon] 2017 （ ISBN:9789811067921 ）
MISC
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特集＝ あの頃に出会った定理「多様体上の1の分割の存在定理／大域と局所の結節点」
野坂 武史
数学セミナー 2023.9
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群による結び目の研究
野坂 武史
数理科学 2020.3
Research Projects
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Various studies of Chern-Simons theory from 3-dimensional geometric cohomology
Grant number：24K06708 2024.4 - 2027.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Grant amount：\3510000 （ Direct Cost: \2700000 、 Indirect Cost：\810000 ）
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Nilpotent study of 3-dimensional topology
Grant number：20K03605 2020.4 - 2023.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Grant amount：\3120000 （ Direct Cost: \2400000 、 Indirect Cost：\720000 ）
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Algebraic topology of quandles, and its application to low dimensional topology
Grant number：17K05257 2017.4 - 2020.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Nosaka Takefumi
Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）
The purpose of this study is to analyze quandle, which is an algebraic system, and to give its applications to the field of topology. In this study, I investigate quandles from the viewpoints of manifolds and nilpotent methods, and obtained some results. Meanwhile, given a quandle, a (co)-homology theory is defined; from the viwpoints, I calculate quandle cohomology with smoothness and the second cohomology.
In applications to topology, I gave a procedure of computing the fundamental 3-class of a 3-dimensional manifold. If the manifold is a knot complement or we are give a nilpotent setting, I showed that the procedure can be described as a concrete formula. I also gave some results on centrality of meta-nilpotent quotient groups of the free group. -
Characteristic classes of quandles, and its applications to low dimensional topology
Grant number：25800049 2013.4 - 2017.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)
Takefumi Nosaka
Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）
The subject of this research is "a quandle", which is an algebraic system. The purpose is to explore quandle theory from broad viewpoints and by many means.
I gave some applications to low dimensional topology, including 3-manifold, (surface) knots, branched covering space, Lefschetz fibrations, and surface braids. The study of quandle contains many mysterious areas; however, I showed that homotopy theory, group cohomology, bordism groups, invariant theory, algebraic K-theory are useful to quandle theory. Furthermore, as an unexpected development, I also pointed out that quandle theory is compatible with secondary characteristics, bilinear forms, and cup products.
Teaching Experience
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ベクトル解析
2024.10 - 2025.3
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Linear algebra
2018.4 Institution：Tokyo Institute of Technology