Norio Iwase | Last modified date：2019.02.25 |

Graduate School

Undergraduate School

Homepage

##### http://www2.math.kyushu-u.ac.jp/~iwase/index-e.html

Academic Degree

DSc at Kyushu University

Field of Specialization

Topology

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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