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
Famous quotes containing the word significance:
“Of what significance the light of day, if it is not the reflection of an inward dawn?—to what purpose is the veil of night withdrawn, if the morning reveals nothing to the soul? It is merely garish and glaring.”
—Henry David Thoreau (1817–1862)