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Tag: surface groups

The commutator subgroups of surface groups

Every subgroup of infinite index in a surface group is a free group. There are many ways to see this, for instance, using a bit of topology. An infinite index subgroup corresponds to a covering space with infinitely many sheets and this covering space is a non-compact surface. By a result of Whitehead it deformation … Continue reading "The commutator subgroups of surface groups"
Author Steffen KionkePosted on 18.01.202118.01.2021

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