Morse不等式的一个新证明

A New Proof of Morse Inequalities

用Witten形变理论在带边微分流形上给出Morse不等式一个新的证明方法.首先,说明了相切型Morse函数很自然地与带边流形的Hodge理论相结合;然后,利用Witten形变给出算子ΔT在临界点的性态,进而证明了定理.

Witten deformation theory is applied to a new proof of the Morse inequalities on a differentiable manifold with boundary. It is explained that the tangential Morse function is naturally combined with the Hodge theory of the manifold with boundary, then, Witten deformation gives the behavior of ΔT at critical point, and thus the theorem is proved.