Topological Significance
The sign of the Yamabe invariant of holds important topological information. For example, is positive if and only if admits a metric of positive scalar curvature. The significance of this fact is that much is known about the topology of manifolds with metrics of positive scalar curvature.
Read more about this topic: Yamabe Invariant
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“History is the interpretation of the significance that the past has for us.”
—Johan Huizinga (1872–1945)