**SMS scnews item created by James East at Thu 26 Feb 2009 1333**

Type: Seminar

Distribution: World

Expiry: 6 Mar 2009

**Calendar1: 6 Mar 2009 1205-1255**

**CalLoc1: Carslaw 375**

Auth: jamese@pisa.maths.usyd.edu.au

### Algebra Seminar

# Indecomposable $PD_3$-complexes with virtually free fundamental group

### Hillman

The Sydney University Algebra Seminar resumes next Friday March 6. The first seminar
will be given by Jonathan Hillman -- title and abstract are below.

There are plenty of empty slots in the schedule, so please contact me if you (or any of
your visitors) would like to give a seminar. I would especially appreciate some
volunteers to fill a couple of slots in March.

---------------------------------------------------------------------

In his 1997 thesis John Crisp showed that if a $PD_3$-complex $X$ with fundamental group
$\pi$ is indecomposable then either the universal cover of $X$ is contractible or $\pi$
has a free subgroup of finite index. Several years ago in this seminar I described the
first ``exotic" example: $\pi=S_3*_{Z/2Z}S_3$. In this talk we shall use one of Crisp's
subsidiary results to determine the "generic" virtually free groups that arise in this
way. (One case has resisted eviction or confirmation of tenure.) The methods are
substantially group theoretic, and not particularly difficult (although I shall use the
notion of ``graph of groups", which may be less familiar).

---------------------------------------------------------------------

After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East jamese@maths.usyd.edu.au