Kyushu University Academic Staff Educational and Research Activities Database
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Norio Iwase Last modified date:2019.02.25

Graduate School
Undergraduate School

Academic Degree
DSc at Kyushu University
Field of Specialization
Outline Activities
Research Activity:
The number of critical points of a smooth function from a manifold M is bounded by a homotopy-theoretical invariant cat(M) the Lusternik-Schnirelmann category. Similarly to it, M. Farber introduced an invariant called Topological Complexity measuring how a space is complex, which opened the door to apply algebraic topology to the world outside mathematics. Quite recently, I am interested in Chen-Souriau differentiable spaces which enables us to introduce differentiable structures in every topological spaces. Currently, I am investigating homotopy-theoretical properties of L-S category and Topological Complexity by calculating L-S categories for Lie groups and total spaces of fibre bundles.
Education Activity:
Lectures on linear algebra and/or Analysis for first and/or second year classes, and lectures on Topology for graduate and/or undergraduate classes. Sometimes are given. Seminar courses are sometimes given for graduate and/or undergraduate students.
Research Interests
  • de Rham theory on diffeological spaces
    keyword : Diffeological space
  • Topological Complexity of Configuration Spaces of Robot Arms
    keyword : Topological Complexity
  • Homotopy Theory from the categorical point of view
    keyword : square ring, 2-category
    2002.04Homotopy theory from the category-theoretical view point.
  • L-S category of a manifold
    keyword : Lusternik-Schnirelmann category
    2000.04L-S category of manifolds.
  • Ganea conjecture for a co-Hopf space
    keyword : Ganea conjecture, co-Hopf space
    1990.04The Ganea conjecture on co-Hopf spaces.
Academic Activities
1. The Ganea conjecture and recent progress on Lusternik-Schnirelmann category
[translation of Sūgaku 56 (2004), 281–296], Sugaku Expositions, 20(2007)..
1. Norio Iwase, Akira Kono, Lusternik-Schnirelmann category of Spin(9), Transactions of the American Mathematical Society, 359 (2007), 1517–1526, 2007.06.
2. Norio Iwase, Mamoru Mimura, Tetsu Nishimoto, Lusternik-Schnirelmann category of non-simply connected compact simple Lie groups, Topology and its Applications, 10.1016/j.topol.2004.11.006, 150, 1-3, 111-123, 2005.06.
3. Norio Iwase, Mamoru Mimura, L-S categories of simply-connected compact simple Lie groups of low rank, Progress Math., 215, 199-212, 215, 199--212, 2004.01.
4. Norio Iwase, Lusternik-Schnirelmann category of a sphere-bundle over a sphere, Topology, 10.1016/S0040-9383(02)00026-5, 42, 3, 701-713, 42, 701--713, 2003.01.
5. Norio Iwase, A_infinity-method in Lusternik-Schnirelmann category, Topology, 10.1016/S0040-9383(00)00045-8, 41, 4, 695-723, 41, 695--723, 2002.01.
6. Norio Iwase, Co-H-spaces and the Ganea conjecture, Topology, 10.1016/S0040-9383(99)00052-X, 40, 2, 223-234, 40, 223--234, 2001.01.
7. Norio Iwase, Ganea's conjecture on Lusternik-Schnirelmann category, Bull. London Math. Soc., 10.1112/S0024609398004548, 30, 623-634, 30, 623-634, 1998.01.
8. Norio Iwase, Mamoru Mimura, Higher homotopy associativity, Proceeding of Arcata conference, Lec. Not. Math., 1370, 193-220, 1370, 193--220, 1989.01.
9. Norio Iwase, H-spaces with generating subspaces, Proc. Roy. Soc. Edinburgh, 111, 199-211, 111A, 199--211, 1989.01.
10. Norio Iwase, On the K-ring structure of X-projective n-space, Mem. Fac. Sci. Kyu. U. Math., 38, 285--297, 1984.01.
Works, Software and Database
1. .
1. Lusternik-Schnirelmann category.
2. Lusternik-Schnirelmann category and an A_infinity structure.
3. Norio Iwase, Recent progress on Lusternik-Schnirelmann category, International Conference on Topology and its Applications Joined with 2nd Japan-Mexico Topology Symposium "Topology in Matsue", 2002.06.
4. The Ganea conjecture and its counter examples.
5. Norio Iwase, Some problems by Ganea and their p-localised versions, JAMI (The Japan-U.S. Mathematics Institute) 2000 Program "Recent Progress in Homotopy Theory", 2000.03.
6. A_infinity-method in L-S category.
Educational Activities
My Education activities often (not always) includes the following four.
1. Supervising graduate students in master and/or doctor courses.
2. Supervising 3rd-year and/or 4th-year undergraduate students.
3. Basic and/or advanced classes on Topology.
4. Lectures and/or tutorial classes on first and/or second year undergraduate students.
Professional and Outreach Activities
Extension Lecturer at Faculty of Mathematics, Kyushu University (July, 2006)
Member of the Committee of Extension Course of Faculty of Mathematics, Kyushu University (April, 2008 - ).