ASPECTS OF MORSE THEORY.

Title: ASPECTS OF MORSE THEORY.
Identifier: AAI8423073
identifier: 8423073
Creator: KALISH, DIANA.
Contributor: Edgar Feldman
Date: 1984
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In this paper the Morse Index Theorem is proven in the case where two submanifolds, P and Q, are at the endpoints of a geodesic. The index of the Hessian of the energy function is computed on the space of continuous piecewise smooth paths using P-focal points along the geodesic and a boundary condition at Q.;The Fundamental Theorem of Morse Theory is then generalized to the above case to obtain, under certain conditions, the homotopy type of the space of continuous paths joining P and Q as a countable CW-complex with a cell of dimension (lamda) for each geodesic from P to Q of index (lamda). The description of the index of a geodesic in terms of P-focal points and a Q-boundary condition involving the second fundamental form of Q lends itself, in certain instances to a simple computation. Several such examples are worked out.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.
Program: Mathematics