Norio Iwase | Last modified date：2023.03.11 |

Graduate School

Undergraduate School

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Academic Degree

DSc at Kyushu University

Country of degree conferring institution (Overseas)

No

Field of Specialization

Topology

Total Priod of education and research career in the foreign country

01years03months

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.

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

**Research Interests**

- de Rham theory on diffeological spaces

keyword : Diffeological space

2013.10. - Topological Complexity of Configuration Spaces of Robot Arms

keyword : Topological Complexity

2008.02. - 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**

**Reports**

1. | The Ganea conjecture and recent progress on Lusternik-Schnirelmann category [translation of Sūgaku 56 (2004), 281–296], Sugaku Expositions, 20(2007).. |

**Papers**

**Presentations**

Educational

**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.

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.

Social

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