Foundations of Morse Theory and Applications : Critical Point Theory and Geometric Analysis

ISBN-13: 9783659283659 / Angielski / Miękka / 2012 / 72 str.

Guy Degla; Rachidi B. Salako

Opis

The Morse theory is a sophisticated approach to explore the shape of a manifold by studying certain of its real-valued functions which can be expressed as non-degenerate canonical quadratic forms in some local coordinate systems about their critical point. In this project, we focus on the basic theorems of Morse Theory including Reeb's result which states that every compact finite dimensional smooth manifold that admits a smooth function with exactly two critical points which are both non-degenerate, is homeomorphic to a sphere.

O autorze

PhD Functional Analysis and Applications, SISSA, Trieste, Italy.Researcher at the African University of Science and Technology (AUST), Abuja, Nigeria, and at the Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo, Benin.Joint Project with R. B. Salako (PhD Student, AUST).