| Abstract: |
A finitely generated residually finite group G is called profinitely
rigid, if for any other finitely generated residually finite group H,
whenever the profinite completions of H and G are isomorphic, then H
is isomorphic to G. In this talk we will review what is known about
this in the context of groups arising in low-dimensional geometry and
topology. We will then discuss some recent work that constructs
finitely presented groups that are profinitely rigid amongst finitely
presented groups but not amongst finitely generated one.
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