R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Asympototic Behavior of The Density Function of Witten Laplacian on Compact Manifolds
Ching-Hsien Lee (National Taiwan University)
Abstract:
Morse Theory, which was first introduced by Martson Morse, relates the topology of a comopact, smooth manifold with critical points of smooth functions on it ingeniously. Originally, Morse proved it by the approach from algebraic topology viewpoint. Yet, I am going to introduce Witten's analytic approach and described the behaviours of eigenforms of Witten Lapalacian on the manifold, which gives us the important relation between Betti numbers and indices of the critical points.