Indecomposable $PD_3$-complexes with virtually free fundamental group

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.

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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).

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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