### 数理情報科学特別講義Ｉ   Special Lecture on Mathematical and Information Sciences I

Bowditch Brian Haywa

5541
シラバス更新日
2014年3月31日

2014年3月31日
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### 講義概要

Geometric group theory.
The general aim of geometric group theory is to apply geometric ideas to the study of groups.
It takes inspiration from ideas in low dimension topology, notably as 3-manifold theory,
as well as riemannian geometry, for example, hyperbolic geometry. There was much activity in these
areas in the late 70s and 80s arising from Thurston's geometrisation programme for 3-manifolds.
A major influence was the work of Gromov, notably on hyperbolic groups and asymptotic invariants.
Since then it has grown into a major field in its own right, and has found application in diverse branches
of mathematics.

### 講義の目的

We will give a general introduction to the basic ideas of geometric group theory.
We aim to give the fundamentals of the theory of hyperbolic groups.
It will broadly follow the scheme of my MSJ memoirs, listed below.
Depending on time, we may include extra material on Dehn functions and related topics.

### 講義計画

eneral Course syllabus:
Free groups, group presentations, Cayley graphs, quasi-isometries, brief survey of fundamental groups and hyperbolic geometry
(according to background), hyperbolic groups, Dehn functions. Other topics depending on time remaining.
First Lecture:
General introduction to the course, basic notation and terminology, generating sets, free groups.
Second Lecture: Group presentations.
I will post more details once the course begins.

### 教科書・参考書等

Brian H. Bowditch ``A course on geometric group theory'', MSJ Memoirs Volume 16.
Mathematical Society of Japan, Tokyo, (2006).
Pierre de la Harpe ``Topics in geometric group theory'', Chicago Lectures in Mathematics.
University of Chicago Press, Chicago, IL, (2000).
Martin Bridson, Andre Haefliger, ``Metric spaces of non-positive curvature'',
Grundlehren der Mathematischen Wissenschaften, Vol 319, Springer-Verlag, Berlin, 1999.

### 関連科目・履修の条件等

Required background: Basic group theory, topology, metric space theory.
Some knowledge of fundamental groups and covering space theory, as well as hyperbolic geometry
may be helpful, but not essential. I will review these topics during the course as required.

### 成績評価

Assessed exercises towards end of course.
(Details to decided later.)

### 連絡先（メール、電話番号）

Email: bowditch.b.aa＠m.titech.ac.jp
Room 1107.

### オフィスアワー

Students are welcome to come looking for me at any time.
I may post specific hours later.