Perforated surfaces are classified via surface classification; their connected coverings arise from surface coverings, and their fundamental groups (along with those of the Sierpiński and Menger curves) are large and non-Hopfian.
Abelian groups
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On the fundamental groups of perforated surfaces
Perforated surfaces are classified via surface classification; their connected coverings arise from surface coverings, and their fundamental groups (along with those of the Sierpiński and Menger curves) are large and non-Hopfian.