Connecting homomorphism

Definition
The term connecting homomorphism is used generally for a homomorphism from a $$n^{th}$$ homology group (respectively, homotopy group) to a $$(n-1)^{th}$$ homology group (respectively, homotopy group) occurring typically inside a long exact sequence.

Mathematically, it is used for the homomorphism arising as a consequence/conclusion of the snake lemma.