In mathematics, circle-valued Morse theory studies the topology of a smooth manifold by analyzing the critical points of smooth maps from the manifold to the circle, in the framework of Morse homology. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and A differentiable manifold is a type of Manifold that is locally similar enough to Euclidean space to allow one to do Calculus. Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the In Mathematics, specifically in the field of Differential topology, Morse homology is a Homology theory defined for any smooth Manifold. It is an important special case of Sergei Novikov's Morse theory of closed one-forms. "Morse function" redirects here In another context a "Morse function" can also mean an Anharmonic oscillator. In Linear algebra, a one-form on a Vector space is the same as a Linear functional on the space
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