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"I never realized that I beat a No. 1," Coin said.
Moreover the following sequence of groups 1 → coin τ α φ ′, ψ ′ → i 1 coin τ α φ, ψ → u 1 coin τ α ̄ φ ̄, ψ ̄. is exact.
Now for any pair of covering transformations α, β ∈ A M ̃ 2, p 2, if p 1 Coin α f ̃, g ̃ ∩ p 1 Coin β f ̃, g ̃ ≠ ∅, then one can show that p 1 Coin α f ̃, g ̃ = p 1 Coin β f ̃, g ̃ and that there exists γ ∈ A M ̃ 1, p 1 such that β = g× αf× -1.
It then suffices to prove that δ ̄ - 1 δ ̄ ′ ∈ u 1 coin τ γ α φ, ψ.
Then for any α ∈ A M ̃ 2, p 2, the set p 1 Coin α f ̃, g ̃ is by definition a coincidence class of f, g.
Then by assumption, p 1 Coin α f ̃, g ̃ is an essential coincidence class, where p1 : G1 → M1 is the natural covering projection.
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CEO of Professional Science Editing for Scientists @ prosciediting.com