Special Lecture on Mathematical and Information Sciences I

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Bowditch Brian 
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Spring Semester

Outline of lecture

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.

Purpose of lecture

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.

Plan of lecture

General 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.

Textbook and reference

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.

Related and/or prerequisite courses

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.


Exercises will be handed out in Lecture 15 (14th July) to be completed by 22nd July.

Contact Information

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

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