Homotopy excision theorem

In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory. More precisely, let ( X ; A , B ) {\displaystyle (X;A,B)} be an excisive triad with C = A ∩ B {\displaystyle C=A\cap B} nonempty, and suppose the pair ( A , C ) {\displaystyle (A,C)} is ( m − 1 {\displaystyle m-1} )-connected, m ≥ 2 {\displaystyle m\geq 2} , and the pair ( B , C ) {\displaystyle (B,C)} is ( n − 1 {\displaystyle n-1} )-connected, n ≥ 1 {\displaystyle n\geq 1} .

Source: Wikipedia — Homotopy excision theorem (CC BY-SA 4.0)

Homotopy excision theorem

In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory. More precisely, let ( X ; A , B ) {\displaystyle (X;A,B)} be an excisive triad with C = A ∩ B {\displaystyle C=A\cap B} nonempty, and suppose the pair ( A , C ) {\displaystyle (A,C)} is ( m − 1 {\displaystyle m-1} )-connected, m ≥ 2 {\displaystyle m\geq 2} , and the pair ( B , C ) {\displaystyle (B,C)} is ( n − 1 {\displaystyle n-1} )-connected, n ≥ 1 {\displaystyle n\geq 1} .

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Source: Wikipedia "Homotopy excision theorem" · CC BY-SA 4.0

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