Let $F$ be a finitely generated free group, $\bar{F}$ an isomorphic

copy of $F$, $W$ a word in $F$ and $\bar{W}$ its copy in $\bar{F}$.

A Baumslag double is a free product of $F$ and $\bar{F}$ amalgamated

via $\bar{W}=W$. For example, an orientable surface group of genus 2

is a Baumslag double, and it is known that a Baumslag double is a

hyperbolic group if and only if $W$ is not a proper power of in F.

We will discuss what conditions make fundamental groups of orientable

and nonorientable surfaces of finite genus embed into Baumslag

doubles, and also present recent results concerning the Surface Group

Conjecture, which states: Suppose that G is a non-free, non-solvable

one-relator group such that every subgroup of finite index is again a

one-relator group and every subgroup of infinite index is a free

group. Then G is a surface group.

When? | 15.05.2012 17:15 |
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Where? | PER 08 Phys 2.52 Chemin du Musée 3 1700 Fribourg |

Contact | Department of Mathematics isabella.schmutz@unifr.ch |