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Fundamental group after attaching a 2-cell

Attaching a disc to

X

along a based loop

α

kills precisely the normal closure of its homotopy class:

π_{1} (X \cup_{α} D^{2}) ≅ π_{1} (X) / ⟨ ⟨[α]⟩ ⟩ .

Table of contents 108 2
- Presentation complex Fundamental group after attaching a 2-cell 86 1
  - Presentation complex for the symmetric group on three letters Presentation complex 55

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