The triviality condition is a requirement in the context of h-cobordism that ensures two manifolds are considered equivalent if their structure can be smoothly transformed into one another through a series of simple steps. This condition implies that if two manifolds satisfy the triviality condition, they share the same homotopy type and can be regarded as 'the same' for certain topological purposes. Understanding this concept is crucial for applying the h-cobordism theorem to establish relationships between different manifolds.
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