Connected sum of simply connected manifolds is simply connected

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Statement

Suppose n is a natural number. Suppose M_1 and M_2 are Simply connected manifold (?)s (in other words, they are both manifolds that are Simply connected space (?)s, i.e., they are both path-connected spaces with trivial Fundamental group (?)) of dimension n. Let M_1 \# M_2 denote the Connected sum (?) of these manifolds. Then, M_1 \# M_2 is also a simply connected manifold.

Related facts

Similar facts

Facts used

  1. Point-deletion inclusion induces isomorphism on fundamental groups for manifold of dimension at least two
  2. Seifert-van Kampen theorem

Proof

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